{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ADKY4re5Kx-5"
      },
      "source": [
        "##### Copyright 2019 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "S2AOrHzjK0_L"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "56dF5DnkKx0a"
      },
      "source": [
        "# Approximate inference for STS models with non-Gaussian observations\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/STS_approximate_inference_for_models_with_non_Gaussian_observations\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "laPe5xoS42ob"
      },
      "source": [
        "This notebook demonstrates the use of TFP approximate inference tools to incorporate a (non-Gaussian) observation model when fitting and forecasting with structural time series (STS) models. In this example, we'll use a Poisson observation model to work with discrete count data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4YJz-JDu0X9E"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "import tensorflow.compat.v2 as tf\n",
        "import tensorflow_probability as tfp\n",
        "\n",
        "from tensorflow_probability import bijectors as tfb\n",
        "from tensorflow_probability import distributions as tfd\n",
        "\n",
        "tf.enable_v2_behavior()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YagBskFAO34k"
      },
      "source": [
        "## Synthetic Data\n",
        "\n",
        "First we'll generate some synthetic count data:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OKgRbodJ4EuU"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f940ae958d0>]"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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XtXTyyrZKbr8o9+R7Yuw2Lp5kvTr5cB2dAM74GFzOOB25olQUGlMt8mA6NeV/6Dr5bzYe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\nKWVxmsiVUsri/j/yoJE+Mbrs0wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "num_timesteps = 30\n",
        "observed_counts = np.round(3 + np.random.lognormal(np.log(np.linspace(\n",
        "    num_timesteps, 5, num=num_timesteps)), 0.20, size=num_timesteps)) \n",
        "observed_counts = observed_counts.astype(np.float32)\n",
        "plt.plot(observed_counts)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OH2nvBuOxDrd"
      },
      "source": [
        "## Model\n",
        "\n",
        "We'll specify a simple model with a randomly walking linear trend:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hSsekKzIwsg6"
      },
      "outputs": [],
      "source": [
        "def build_model(approximate_unconstrained_rates):\n",
        "  trend = tfp.sts.LocalLinearTrend(\n",
        "      observed_time_series=approximate_unconstrained_rates)\n",
        "  return tfp.sts.Sum([trend],\n",
        "                     observed_time_series=approximate_unconstrained_rates)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iY-pH3hQz0Vp"
      },
      "source": [
        "Instead of operating on the observed time series, this model will operate on the series of Poisson rate parameters that govern the observations.\n",
        "\n",
        "Since Poisson rates must be positive, we'll use a bijector to transform the\n",
        "real-valued STS model into a distribution over positive values. The `Softplus`\n",
        "transformation $y = \\log(1 + \\exp(x))$ is a natural choice, since it is nearly linear for positive values, but other choices such as `Exp` (which transforms the normal random walk into a lognormal random walk) are also possible."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Hg_B4tofzxgc"
      },
      "outputs": [],
      "source": [
        "positive_bijector = tfb.Softplus()  # Or tfb.Exp()\n",
        "\n",
        "# Approximate the unconstrained Poisson rate just to set heuristic priors.\n",
        "# We could avoid this by passing explicit priors on all model params.\n",
        "approximate_unconstrained_rates = positive_bijector.inverse(\n",
        "    tf.convert_to_tensor(observed_counts) + 0.01)\n",
        "sts_model = build_model(approximate_unconstrained_rates)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Pxua5B2wxIMz"
      },
      "source": [
        "To use approximate inference for a non-Gaussian observation model,\n",
        "we'll encode the STS model as a TFP JointDistribution. The random variables in this joint distribution are the parameters of the STS model, the time series of latent Poisson rates, and the observed counts.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vquh2LxgBjfy"
      },
      "outputs": [],
      "source": [
        "def sts_with_poisson_likelihood_model():\n",
        "  # Encode the parameters of the STS model as random variables.\n",
        "  param_vals = []\n",
        "  for param in sts_model.parameters:\n",
        "    param_val = yield param.prior\n",
        "    param_vals.append(param_val)\n",
        "\n",
        "  # Use the STS model to encode the log- (or inverse-softplus)\n",
        "  # rate of a Poisson.\n",
        "  unconstrained_rate = yield sts_model.make_state_space_model(\n",
        "      num_timesteps, param_vals)\n",
        "  rate = positive_bijector.forward(unconstrained_rate[..., 0])\n",
        "  observed_counts = yield tfd.Poisson(rate, name='observed_counts')\n",
        "\n",
        "model = tfd.JointDistributionCoroutineAutoBatched(sts_with_poisson_likelihood_model)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R-3amgmKhYn1"
      },
      "source": [
        "### Preparation for inference\n",
        "\n",
        "We want to infer the unobserved quantities in the model, given the observed counts. First, we condition the joint log density on the observed counts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rSj7blvWh1w8"
      },
      "outputs": [],
      "source": [
        "pinned_model = model.experimental_pin(observed_counts=observed_counts)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tFpiyBjFf8Q3"
      },
      "source": [
        "We'll also need a constraining bijector to ensure that inference respects the constraints on the STS model's parameters (for example, scales must be positive)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZVajaBpLf8h0"
      },
      "outputs": [],
      "source": [
        "constraining_bijector = pinned_model.experimental_default_event_space_bijector()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "25nJYyx-nW2T"
      },
      "source": [
        "## Inference with HMC\n",
        "\n",
        "We'll use HMC (specifically, NUTS) to sample from the joint posterior over model parameters and latent rates.\n",
        "\n",
        "This will be significantly slower than fitting a standard STS model with HMC, since in addition to the model's (relatively small number of) parameters we also have to infer the entire series of Poisson rates. So we'll run for a relatively small number of steps; for applications where inference quality is critical it might make sense to increase these values or to run multiple chains."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "NMPlVBk6PcpT"
      },
      "outputs": [],
      "source": [
        "#@title Sampler configuration\n",
        "\n",
        "# Allow external control of sampling to reduce test runtimes.\n",
        "num_results = 500 # @param { isTemplate: true}\n",
        "num_results = int(num_results)\n",
        "\n",
        "num_burnin_steps = 100 # @param { isTemplate: true}\n",
        "num_burnin_steps = int(num_burnin_steps)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mhSe-GFDPg9o"
      },
      "source": [
        "First we specify a sampler, and then use `sample_chain` to run that sampling\n",
        "kernel to produce samples."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "15ue-mBGdcmh"
      },
      "outputs": [],
      "source": [
        "sampler = tfp.mcmc.TransformedTransitionKernel(\n",
        "    tfp.mcmc.NoUTurnSampler(\n",
        "        target_log_prob_fn=pinned_model.unnormalized_log_prob,\n",
        "        step_size=0.1),\n",
        "    bijector=constraining_bijector)\n",
        "\n",
        "adaptive_sampler = tfp.mcmc.DualAveragingStepSizeAdaptation(\n",
        "    inner_kernel=sampler,\n",
        "    num_adaptation_steps=int(0.8 * num_burnin_steps),\n",
        "    target_accept_prob=0.75)\n",
        "\n",
        "initial_state = constraining_bijector.forward(\n",
        "    type(pinned_model.event_shape)(\n",
        "        *(tf.random.normal(part_shape)\n",
        "          for part_shape in constraining_bijector.inverse_event_shape(\n",
        "              pinned_model.event_shape))))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jvriVTPlih3B"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Inference ran in 24.83s.\n"
          ]
        }
      ],
      "source": [
        "# Speed up sampling by tracing with `tf.function`.\n",
        "@tf.function(autograph=False, jit_compile=True)\n",
        "def do_sampling():\n",
        "  return tfp.mcmc.sample_chain(\n",
        "      kernel=adaptive_sampler,\n",
        "      current_state=initial_state,\n",
        "      num_results=num_results,\n",
        "      num_burnin_steps=num_burnin_steps,\n",
        "      trace_fn=None)\n",
        "\n",
        "t0 = time.time()\n",
        "samples = do_sampling()\n",
        "t1 = time.time()\n",
        "print(\"Inference ran in {:.2f}s.\".format(t1-t0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FwE0yWm_2_kE"
      },
      "source": [
        "We can sanity-check the inference by examining the parameter traces. In this case they appear to have explored multiple explanations for the data, which is good, although more samples would be helpful to judge how well the chain is mixing."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LPOVTbboAtGr"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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+yj3hCeV76uiIYXoxPXUmkEk30lKdrbmlurTy/M6a1gpLwkhYqU4BnrVfemib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\n2+l4LNWFYl0UIDlofWzempKv4c5mWN+lK2FbZ96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qgqZwv7lsi2e/6VkftecwPPudE9Hc\nkE0UT7IzoRoojtxjKJobMugfZ2GRCHqipVqiu39IHEt1SCnS98nBoK4g3/vmSnzhn68HXqdQEIH+\n1KosYQQdYbJGSznLcv+I0VZe8s8Zjoua6Se02jPoui942rJ/cJ7qEvEsvZvgpcrKUNA6GpM7x5dP\nmOBRlB+fuxYfmzzakyYOUCzVhnpmWijFVPFLLZamyp00CClIjgz5fxORW6nCIshVq3NYDlFz9o9g\nC7g8LgWWaunS8bC2bary+ToA18U9l4nGk/3Dt/hL+DuWSnUuG2yplpeIq1Rvae9Gd6GIXQZ408gl\ntTS7gYrSUl2apVytkpmMP6e8HMTGne2RhLp/aIGKevsTFuOhTm2nrG+uO66lmnDrxYcjXyzGWlgk\nily2J/pU224JAX1tmIFH4nPDVBbX0duDsMdstFQHHx5ImBuo535ycF6OpT/GMY/PW6vI4T9DpjFu\nzJUes1UL2FJdIuorT9I5yMrjs3ipSrJdiA/QVkCTSpqwLdWXn7infS2vT7V+vzirJpU62jNaqkvI\njmG8Nvl9Twnkc/8w3Umepvqfl7P4i7eTjjdo8LyPntWH9FrKtZCprgb6teIEKkpLdVRckkyhGXXc\nYdc8icN/8ZT//IQ+0a77R7ak8yXePPOWpVq1mMsVFTPJDNUeH2+97qn5wgnAGz861bM/bFZAHXzX\nyzeTiM4govlEtICIrjDsv5CIZtt/LxPRgbWQy3F1gGXIkJlhyiXXAy3V8lnIAaJepOIsuOJ3w5Tu\nH/7rhbmHWQPzjDcNr3Z4VH8etN+01bXCl0HCk9XicdurS3HEL55yXOLURW8ADlTs0RSLwilgXj/B\n+NfIGizV8OrUSlSw9/Vks16XhqMmDAWguH8Y7mf2qY4WeN6qbZHHAAE+1SjDUq0GBBoaG8ANRApr\nmNXOUlWwVeQ7jLP4i64sJB2E6Kvv7QwUigJ3v74iVR1oub6ceqCiWg6i6lWhKJwgo2ifakvOsGle\neU3z+ckszU6gYrlKtSZOgy+nfGkrKqopRfV3mNcygwxuacQr3z8J/W3/37Cg0KC2oVbEXIhpMYDj\nhRAHALgKwA21kM11/6isZTCbydTUUl2JVysv4RQ97ZnkYyie+k/2Bip6rxf2zB1LtbJNn42JtQCM\nYdvbq7fhFw+/7WnXXCt88gcppUpav9Tjf3jvW1izrcNxSfPNEKbMYsVKdQLOv2EaJvzAmjFXy0gi\nS7XdSXZpHY3a8EsFTO9QcxnCe2tb8fLCjVi1pUNxg5DKob8iJk2pJ3l4TrzsCKZcl3F9jk3oPtU+\nSzVZKfUA9xmamh8pl2qp1l+TaymwLdUhy5l75YrXUCdRuHojt09fhm/9ZxZunba03qI4lNuZ6yn1\n1NcadGVZhLsLReQL8ZYllpZZY/2KQdLsHXqgYsk+1cpDyBD5pvqdeBDyuoos3rADS7SUfypqSlFd\nYfD4VNsPe7eBfZz0gGE6oeP+ocleQz/NyIWYhBAvCyE221+nwcrWU3VMgYqVoNaW6kooXbI4uLPC\n3v2x/JgDEgaQYeYq7JkXikUr+0fIMaUGOj/y1hrc8PwiZ0E5637lW6qTVifT45QDaynPp48cax1b\n+5jXUFipTsD0JW7UqdenOv41ZGVUOy09UNG1VOt+VoTbXl0GAFi5pR056QYR4lNtTqnnP07fFrcz\nNx1HJWjVc1ZsxQ/uneN5rnKaWEe3VJtuNbxfEwBvoKIe1CUVJDf7B+zr+a/olSuZlQ1I3xRVLdhg\nB+Vu3FF6ruVKEyeHaxiqslooFmPFVjiBtfbiL6qlujGbwd8vOsy9hv3ftVTHa6L//doyPDN/nfM9\niaVZCOGUeelaVarS453Rsa4nn1l7VwHrtnWA4DcAnPh/z+KE/3s28LrqKq7D+zc5n99d24r31rkp\nTT3WOzlYDnP/UFzq1F9cQ50v9kJMNp8H8EjQzkou1iQfQeUt1VTT7B+rt3aUfQ1ZruV4zm8Ztn9P\nSEOv75HthRU7lMxSbcUlBLt/RNX/qP5IvV4lVr9MWp1MbWlbV94jjxsrlS44ULFE1M40SQckraJq\nIJDqogAEr5hkRdJ7l+S17h/sU222VJvcG7w0BOSf9l0/KKVewqJ+4Y3TsK0jjyP3GOps0xsOeW1n\nMBHSMP/0g5Owqa0LnzxibKCvtD696RxnuKx6alx/UPWYnVGpluQLRazc0o6Rg/rUWxR0l9lBqBag\nfFF4ylRQM2CVL4G8nVLPGohaZe2M/XfFifuMCLxPUB54ne/dPQcAsOTaswEkW5BKCDiFVZ3hKQV9\npqlBsVRf8LdpmLViK/YfOSDxMuUPz1mDkYP6oDGXcVxUAOC03z3vPVB5XK5bV/QzLAqvK0+haF5x\nrgqYbmJ8MER0Iiyl+pigiwkhboDtHjJ58uSyWp3eYqn+4r+CM2nERbdUB2WgCXf/MFuqTdmAwoqe\nDHYOC1SMNaiO+Qri5OCOvFUZ7h8SGago9SNn1eSUda5sqS4Rr1UjufuHx1IN7+IvugVVkstmPP6D\nslB1F4Ibv6xhoZI4gYq6P3cQgSn1EpbzDrsRUKfXjdk/7DRd6rG67AeOGoi+jTn87dOTcfxewwMt\n0LKx0H2qjdk/lDaKkNxSvTO6f8hffP2zC3H0tU9jexnL3FYKU27zJKidVbEoYlmqs6ql2lbWZFkL\nUppl+2AatMZhzdZ2AHD8isMoCndwkKXylOqiVn9zyuqnM+0Um3KwnPQeK7e0221L8HlqO+oMlkOu\nGRRLXEOlL9ZCTER0AIAbAZwjhNhYC8GcQMUKa9VWRpie1R5KaYPil0rJDe34VJN/4BcVqOjPU+09\nprM73P0jidHLTQhQ+jtLemaY7UPWTSdxQ4kyVYtYmlNao5PriddfNv55siB4fKo1S7VeaNRzVX9C\n3Q3CmFLPZKk2KdUBcpZCwhS0ANxpdXV6PShLgptBxXwtXdEPslQ7PtUxFn/Rp7WTRzOnrerXnh0p\nUKrLnXZW3RDi+lRLRTVfFJalWkmh1RAweJUzUht3dOHy270L1QTlplZZY0957zKwOeJIq17I8u1a\nfyJPM+I9zfKp1n2gCVa6vVLuEdW2mKx3YUphUJ2vYWBxnEWcxgC4B8CnhBDv1kow1T2hkvTE7B+y\ngAS5WpazoqLJp9pkrFLvFbaiIhDP/WPiLv082zwDTOX0SgyAkvtUWyec8tvnfPukPFnXWpYqIpXq\nNEcn1xNP8o4EJUYWhPauAp56ey2EbSXyBCpKC6rBp9rr/uH1qS7H/UPfFHfa2URYZY9CVaopwP0j\naoranFrQECii5AkFIhZ/8UxrJ/e5rMSy0z0O7TmWuvR1JSn3PagzTAXNUr2lrdt4jiyO+aK0VGcc\nRSWr1zP7emr5enD2ak/ZXWyvxvqhg3YHYPllS9rtgL712zuRzRCG9G2M/E0eS3UF3T8yZA0afD6Z\nZLm/lNJXU0TmnaQ+1XJXUXOqrpXSF3MRp58AGArgeiKaSUQzaiGbE0hXRntuQi7+krZp+zAcS7Wj\nVHufSbyUeubvptSxYQOZvN2GeE/xntARYakGgF0HNjvuYvoVvO6tRY+8SRCGT/NWbQtdMVK9/wIl\nXkKXp9y2qlrEsVSnNjq5XgghPI1ukpcqK8/U5xbi8/+YgcfmrgEgtBUVzem0GrLe5V11n2qTRcZa\nJti7zZjdQtOqy7FUA14FNknjqfqsZshVdCXzVm1zEuMHdXwm0U0pvNQ8oYBq0fZfVw9UjDMVpl6m\n3AC53kCchr5arN7ajn9NW1q2pbozH6xUA8BWg2KtliurQ3QHzA0B9Uwv2+pg4MPXvwwA2GN4P1x0\n1DgnYwcA/Ph/bznHN2Sj82FLZB11O6p45wVdB1Cyf/iWc5fBw8lvYg2Og/erv1e2HXHcPwS8bWCc\n2YBKIYR4WAixlxBighDiGnvbVLmQkxDiYiHEYCHEQfbf5JrIhepZqoHkA5diUeDqB+dh2ca2ygoU\nwY7OPP7y7EIArvKs16tT9t0FQHhfF+7+4d0XmadaT6mnHd4Rkb3HJKUpAxkQb2GbKNRzz/rjCzjX\nbsOCeHftdrwRoHh36z7VpYtVFeIo1RWLTq5kZHI9Gf/9h/Gxqa843zdu78JbK7fGOldWniV2w/DH\npxYEBirKQjPAXho2Q96pVJ9PteF+2UzGV9HjrKQUx6daX5xGok/RJqmM7V2qUu23VG/c0WVcQMd7\nf5Ol2m8Z82f/CFYo1E2lWKqTrnDXG9AfUXsdlerLb38TP77vrdC0bXFQB30FLVARANq6/S4uTi5k\nO091NpNxrMu5gKXTdGVdLT9b2y3FvbtQtHOmu8dJhSNfELEzh1hBetbnUqw/q7e244zfP4+12zp8\n9UQaAlRLnsxeUBTWuS+8Z+4LHprtT+sZ5Ytt8qkOU1Dk8fqKire8vCTwnJ2FHZ3xFiBKipydSepW\n8N667bjxxcW49NbyAw+T8Nsn3nVkdX2q3Ydy7Yffh08eMRZA6YGK++za37MvzGXJXVHRPUY/ut3Q\nDun4ZoEDZK3ErE0pV/j5/XON253saCHumvUkTqtrervGn6FEJ3/PtF8IcYMQYrIQYvLw4cPjS5lC\nWhX/0KfeWYf3/+nFWOfp5XPe6m0Q8DZcskDLTvG+y44GYFkO1M5JT39lsihkye8faA5U9H6P4/5x\n7sHmsRVp1zN1gjs683hWSQEmaVMUL6Lg4EtLZnsEre83nUTBPm16QFPUoKOUxV92RqVaRx0w1Zo2\nxS0iKU/MW4txVzyEjds7HQtQhqRPtbccmDog18VABhm5dTdoRkgvq6aZjq580ZdFI+PM4hRjZ68o\nCrd8ux1V/PJ9x/TleGdNK+6Yvsyw+ItlCJj63EJnW75QtAemAqf97nl86qbpxuv+6en3fNsowlKt\n/mQ3q0/w8R5LtXLdPzzlv/fOxkf+YlkTKx2oKOMIks4ayfFnqTmYS8UbR+G3VA9paXTLUUjZ1Hep\n2VUOHTsEp+zrZgEKz/5R9Fmqddoi2lpT/fb4VCu7nUDFMrTXkk4NKHeOu6tjqU6XVh1HqU5tdHJP\nxKywebN/uI741vc9hvdDS2MWhYIwWqqD/LysYzKhVtWpzy3E5KufKKlgBlYUTQ7T/a+4Zw4u+vtr\nWKxZDtXGgAyphgC34w8KJjIZ6EzBhdItRrdoma7qt/Ybb+09RvUoS1e9rwn6b66npVrO9mzcnjxn\n9j9sq+W81dswfbHVtLU05oyWalPUuqyXhaKwleqMo1TrcRPycvp1TIOyrkIRGS0PvdomxHXhKgo3\nT3WmBPePBmfGrOgbDFiZHopYtN6t53KpdiHCU/+Z8ptbrld+ZO7q0UP6Ksda/0Mt1bLOF9M3jZwW\nKmyodgw2STPxyNnTWgc5NubcDsXkCnHQmEHO57BZFH/CAK9RZ3cl5WhonuqCKfuH9/i2zqjsH/C9\nWFUHMVmqd3QV8Icn34vlP+6/X/J3FvQE5P2d7B8pq7hxlOrURif3JH52/1w8MW+tOQgOmqXaUard\n12MFKQqjT7UsZKbGpiEbvkz5tY+8gw0GRcPkU7i+tRMbY1j69Mpg+s2L1lsBCNu1TtWb/cN0Nbfj\nV+v2+GEtynlB7h/m5yAHL0GLxAB+d5a0VeQ0ojektbJUz1/T6nuHA/o0ACjNUi071a58EffNtOwJ\nLU05o0+1aaAnS6O0cmVtX2MguBzp17n2kXdw5QPzPNu6bYuvNw2l674R11Itiq4SnSvB/aMhJ/PG\nC7+l2s5YpKZTzBeFY6kOQ29rfvnh9wWm1Dv34JG47eLD8dFD3XCeOPmpndkpVqkDqfTiL059KnH2\nrtZB32ogsBwIqGV3RP9mRyFduy14oZmgFRVNqR+jsn9ktewfuvX+u3fPxoJ1rYHX0O+nb1CbTzmQ\n2Nrejd89+S7ufXNl6HVNlNJfBhU7PftH2gJeI5XqNEcnp42wEfQtLy/BF/45w7ywiPCONJ1Co2zL\nZTMoFIUnUCqrjfhNnZRuyZL3M8ng+S2Ggw675kkcevWT7jn+ywCI54Mnj1nX2oET/+9Z4zFBKfVk\nZbpj+jJnW5NiTQhWqi2F+dG31niCTd0sAdb/j98wzfFblejuLGmLOE4jus9kLSzV9765Aqf//nk7\nANhlQLOlVK/bVoJSnXWVaknfxqxZqTa5f9jFUQ6Ic1k3pV5Qh6Bvv/fNlbj5pcWeztNy/yCP5Uhe\n1/KpjqlUw3VjcXyqtd+xaP32wOA9aXXvKhT9Ac/2PtUinS8UQfDnz9fRb3f0hGGBqfi6C0Ucvecw\no59pmFLoZOUS6euc00KlfapN9SkOMiC/9NU+S8NrqZaZMLSr2c/oby8sDr6/PqulBCoCXh0gOvsH\neZTghev8sSKhcQGGh+HxqVaecUFTWkoZDMmrvbNmW+JzdfQVp9NWa2NFsqQhOvmh2as9fnlpJM5y\nnkGZJdQC7RQaxa9ZWqpVd4kmbcRvmk7LZQibtGlUUyH0WXHLmGLTvb1Mv1ke8/l/zPC5gEhMSfGt\n7f5tXp9ng0y2Zexf05bi0ltfxz1vrPT5karnzV/jHeXri3zEeTo7ex/dna+9Uv343LUAgHWtXuW5\nv+3+sb412ZLF761txTr7HHVA22C7NfgGo8Z6Y7tH5N3pXtWX10RQ9fvWXbOcz90FYftUu/uzziyO\n8KfrC7mXvETO4P4xf00rTvrNc7j+2QXG8+Xqq90F//OQFnl1kJq3s3+EKbGmTDG5bPCiMaa8vPF8\nql3L/E5eXQOptKW6yV4RM9aqfwpSl0sS4HjxP8q37zUYLNWltO1BrmJGt83QQEXbp1o55LzJ/oRr\nw/o1BV5DGO5riusC/DMDpZQHWdfP+P0LynXD33/Qa+5OuftHj1mm/DJ7AYRLj59QZ0mCyRcEohYw\nC1SqlXI6enBfrN7agWZlhJzLWBYptXNqzFq5KmUHZLr2qi3tvm2mzkxv4MrxW9PrnOlS8azZ5mAM\n37S20JRewznSh3OVvdLc2tYOJfuHfYxyXX06TXf/YEt1NF0F7zOshfuHfC/+mQZr+/rWZJbqU5Vl\nsLvyRYzo34ST9x2BWcu3olD0l4MwS3WX0hlIFS5IsQyqfw/PcTNiSEu1imOpLibN/qFZqhW55KDi\nlUUbcflJE33nS6XD7P5h7dOV6qgMOj+4Z45vm1QkTKct3+RPsxbPp9r6L5C+zjktVMtSnTTgUBqt\nNmzvxB+VQNLdBjbjvMmjjec8+fbaEqV0MflU62U3zjMKDpT3HxtWZrvyRTQ3ZD19o+qPLQlTqgG/\n+4fXp9rdrhsLK1UcOroLTtuRZJZIX8cjbTNMPUap7gks3rAD+48cGHqMqbPMF7yW6qmfOhSvLdmE\noUqlyGbIF9FLROjTkHWUFdO1Tf5nps5MHzWW47YWx6c6TsXMEBkbF9MoXr2DyWIvLdVuCi1/9g+1\ncdOt+6rlXs2WwATzykJvvHIt8lRva7fcDNZpFulu+/2V4lMt6bQD8cj2iS4Ui4GrdKrIYiXrWEbJ\nHR+kWAa6hSifuwrFwEUjpN9lHNSUeqZAxaacbVkMyH2rrhKr23ulFVsdtDupAA3qsbCf7/Qlm/z3\nyWbsxV/cbTIbSLNt/VRJYqm+540VGKMEOTIulc7+IWdYr7h7DopC4KGvHosdnXlkiNCn0f8eJWr/\n9tsnvKFbJ+0zwtNfVhKvpdp2/7DLbv8oK5qCLLddhSI+ddOr+O7p+wAwl9OwR97RXURTLhP4Xgb3\nbcDmtu5Qw09U9g/1XF3vKM1S7d/W3l1Af9st764Zy337FxoWfgHcgU2PXqaciUectHomxVd21JIh\nLY04fb9dPcfkMuRJ4yfp05BFhz3iNwZJGct/tPIdx/0jqOPX7ylMfXHMICLTYboBTsDr22ry1ZOW\nalNAqNtIuDt1pVq/X5zRsTxi4oh+uOMLR0Qe35sQQvjcemrh/iHf263TlnlzI9uf1XKe1MWps7uA\nooCzzHi+KPDG0s2eY8Is1Ztt2fo1ZQNTcMnvcWaKTItGyOvKKeI4WANM63POYP2Ri8t0BFgWpSWv\nu+DPhpJz0n56F80hMq+ouNb2eVetg5KsnUZMreu7D+yDgX0a8P8+coDveGfxlzBLtf3/Fw+/E3jM\nzk6lF3+R73bOyq2Yu8rysd3vp49h8tVPhJ6nun1c++H3YeEvzsL/nXcggPAsMuXSqLhR6Zbqp751\nPIB4RiK13L7w3gbXqOMsUqT6VAdfsTNfQFMuG3jP+y8/BgDwk//NDTRkWO4f3m3qV1n/v/ff2bjp\nxcXe4xKUB3mo0WVLGaQ//94G3/7tBn0HUNfxyNjXji9PLegRSvW9b65wPheLAn948r1QpacSrG/t\n9K3cJNNylYPJHyxfFJGVMpshtHb4V2trbsiivSs4gMN0XVm+H5jlZkb0W6rLcf+I41MdTdDstckC\np96i0+CrJfP5knO8f2lm9bKbdT905fpd+WKiYI0vnzgBR04YGvv4uBDRGUQ0n4gWENEVhv0XEtFs\n++9lIjpQ2beEiOZUK7A4b0g3J8tpNdnc5r63HYqFxTR7kbSMdxWKdjo4S/ksCoGv3PFm7GvOsReI\n2ne3AW4qtwA7S7AFGxhhp4+76kP7+zrfnJJ2LHb2D+HKIa/XXRDY98eP4s7py5xtQau0yd+SLxR9\ng80Gw0If0v3DNDD9wj+tothoWBSnIetPsVkUAqfvtwuGtPiXYzdlVfDL7n6udVaJnkKllyk3DZgA\nb301oQ6Ch/VrQjZDTp9sUsAqtSqmKYmAsF02Rwxo9h0jifIZlvuDVkIOojNfRFODvky5S1/F2h80\nuwQY3D+UC8pH9+8Zy30DlkpZqpP61EvcZcrltdNVb1OvVC9avx3f+Pcs5/vLCzfid0++ix/d5/e5\nqySHXfMkjvv1M55tE0b0K+la6ks3du5FETn6y2UyxtF4c0PGGY3G9YOWh6kKgW7dnbV8C75+55sV\nyQlqzEoSo15miIyphUwWOPUZmyzV0jKmPmd90Ry1sdimPWv1N1z/7EKc/cd4i/3o160URJQF8GcA\nZwKYBOACIpqkHbYYwPFCiAMAXAXgBm3/idUKLDZZSGphqW7vLjid9vXPLMA1D83D9s487jGkgUpa\ntju7LfePTIaswGGTa5VxYGu9/xWbLX/+sUNalMGd+V7h+W6BC6aMwYj+zb56JDuqxHmqpaU6KxXo\nAtq7C/jp/XOd5xTkAyvrXneh6BsiSCVffVaW+4f5t8sYkKYgS7WWGlPmvDYhlYSwx6Ceq/v8p62z\nrhcVt1QHrCIahTowG9rPGkT1s90vTH1jpRbcElp5k6tvRrXrP3/AuyKgXqelzCb3jxcXbMDcVVt9\n19zemceWtm7L/SNgsONZpTVARFPRVg8Na39ihmp472fYpra/SYqYdOWTluq0VdPUK9W6P48Mfopa\nMagcghrTUvXLgsdK46/o3QUROkUJWB2KntMZAPo0Zt1ARYOAJuOLyTqmN0CPvLUG981cFZF3M1Rk\n5X4unfkCfnb/XJ/SCgC72qN+SVCgoqkxKwrLFQYwWwj0bANmn2r3unojXcqrd7KLVLpXspgCYIEQ\nYpEQogvAnQDO8d5fvCyEkP4J02At3FQTTFbNO6Yv880AVJrO7iIG2jmp//r8IvzthcV4eYF/ahFI\nrlQXhUCxKJw806bz4wQqNuSU7B+BbU2wbPli0bEA6+2GvEdSn2q9LhQci5xrfQ+yeslzuwp+tyip\npKvPRSokpt8olWmTNbMhkzGs1hrs3mFKVaaj7mnr0up8yjrrulHh5qupoTS1Qy1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1aWluoBzWZLNWnppmQnqbp/tGs+YkFlUG0fSg5UtJ/LP19ZCsD2idSOCbOqEfxKt/wqK74+TWjJ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\nhmEYhmEYpkz+P6HCsuAXnEl4AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1200x400 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "f = plt.figure(figsize=(12, 4))\n",
        "for i, param in enumerate(sts_model.parameters):\n",
        "  ax = f.add_subplot(1, len(sts_model.parameters), i + 1)\n",
        "  ax.plot(samples[i])\n",
        "  ax.set_title(\"{} samples\".format(param.name))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tZOydxU53oE9"
      },
      "source": [
        "Now for the payoff: let's see the posterior over Poisson rates! We'll also plot the 80% predictive interval over observed counts, and can check that this interval appears to contain about 80% of the counts we actually observed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "56rIH8MCeU9F"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f93ffd35550>"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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jjbza+yr9qYOpxEvnX8rZs8+e0Pnzefjqf6xk4dIo77qxZVznyGYFFotkuEBN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\ne+hPmdGagvXDRFKSQggqnZVUOiuL2yyahbcueCtNkSaaok2E02F2Bne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SOydZrDeDg8X8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\nhESFl4iIiEhI/g9UGMkGSmN+TQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1000x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "param_samples = samples[:-1]\n",
        "unconstrained_rate_samples = samples[-1][..., 0]\n",
        "rate_samples = positive_bijector.forward(unconstrained_rate_samples)\n",
        "\n",
        "plt.figure(figsize=(10, 4))\n",
        "mean_lower, mean_upper = np.percentile(rate_samples, [10, 90], axis=0)\n",
        "pred_lower, pred_upper = np.percentile(np.random.poisson(rate_samples), \n",
        "                                       [10, 90], axis=0)\n",
        "\n",
        "_ = plt.plot(observed_counts, color=\"blue\", ls='--', marker='o', label='observed', alpha=0.7)\n",
        "_ = plt.plot(np.mean(rate_samples, axis=0), label='rate', color=\"green\", ls='dashed', lw=2, alpha=0.7)\n",
        "_ = plt.fill_between(np.arange(0, 30), mean_lower, mean_upper, color='green', alpha=0.2)\n",
        "_ = plt.fill_between(np.arange(0, 30), pred_lower, pred_upper, color='grey', label='counts', alpha=0.2)\n",
        "plt.xlabel(\"Day\")\n",
        "plt.ylabel(\"Daily Sample Size\")\n",
        "plt.title(\"Posterior Mean\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GuBYar27YZf6"
      },
      "source": [
        "## Forecasting\n",
        "\n",
        "To forecast the observed counts, we'll use the standard STS tools to build a forecast distribution over the latent rates (in unconstrained space, again since STS is designed to model real-valued data), then pass the sampled forecasts through a Poisson observation model:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v1HuVuk6Qocm"
      },
      "outputs": [],
      "source": [
        "def sample_forecasted_counts(sts_model, posterior_latent_rates,\n",
        "                             posterior_params, num_steps_forecast,\n",
        "                             num_sampled_forecasts):\n",
        "\n",
        "  # Forecast the future latent unconstrained rates, given the inferred latent\n",
        "  # unconstrained rates and parameters.\n",
        "  unconstrained_rates_forecast_dist = tfp.sts.forecast(sts_model,\n",
        "    observed_time_series=unconstrained_rate_samples,\n",
        "    parameter_samples=posterior_params,\n",
        "    num_steps_forecast=num_steps_forecast)\n",
        "\n",
        "  # Transform the forecast to positive-valued Poisson rates.\n",
        "  rates_forecast_dist = tfd.TransformedDistribution(\n",
        "      unconstrained_rates_forecast_dist,\n",
        "      positive_bijector)\n",
        "\n",
        "  # Sample from the forecast model following the chain rule:\n",
        "  # P(counts) = P(counts | latent_rates)P(latent_rates)\n",
        "  sampled_latent_rates = rates_forecast_dist.sample(num_sampled_forecasts)\n",
        "  sampled_forecast_counts = tfd.Poisson(rate=sampled_latent_rates).sample()\n",
        "\n",
        "  return sampled_forecast_counts, sampled_latent_rates\n",
        "\n",
        "forecast_samples, rate_samples = sample_forecasted_counts(\n",
        "   sts_model,\n",
        "   posterior_latent_rates=unconstrained_rate_samples,\n",
        "   posterior_params=param_samples,\n",
        "   # Days to forecast:\n",
        "   num_steps_forecast=30,\n",
        "   num_sampled_forecasts=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MyPFQzV8SOSs"
      },
      "outputs": [],
      "source": [
        "forecast_samples = np.squeeze(forecast_samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iD_kLwF1V3m-"
      },
      "outputs": [],
      "source": [
        "def plot_forecast_helper(data, forecast_samples, CI=90):\n",
        "  \"\"\"Plot the observed time series alongside the forecast.\"\"\"\n",
        "  plt.figure(figsize=(10, 4))\n",
        "  forecast_median = np.median(forecast_samples, axis=0)\n",
        "\n",
        "  num_steps = len(data)\n",
        "  num_steps_forecast = forecast_median.shape[-1]\n",
        "\n",
        "  plt.plot(np.arange(num_steps), data, lw=2, color='blue', linestyle='--', marker='o',\n",
        "           label='Observed Data', alpha=0.7)\n",
        "\n",
        "  forecast_steps = np.arange(num_steps, num_steps+num_steps_forecast)\n",
        "\n",
        "  CI_interval = [(100 - CI)/2, 100 - (100 - CI)/2]\n",
        "  lower, upper = np.percentile(forecast_samples, CI_interval, axis=0)\n",
        "\n",
        "  plt.plot(forecast_steps, forecast_median, lw=2, ls='--', marker='o', color='orange',\n",
        "           label=str(CI) + '% Forecast Interval', alpha=0.7)\n",
        "  plt.fill_between(forecast_steps,\n",
        "                   lower,\n",
        "                   upper, color='orange', alpha=0.2)\n",
        "\n",
        "  plt.xlim([0, num_steps+num_steps_forecast])\n",
        "  ymin, ymax = min(np.min(forecast_samples), np.min(data)), max(np.max(forecast_samples), np.max(data))\n",
        "  yrange = ymax-ymin\n",
        "  plt.title(\"{}\".format('Observed time series with ' + str(num_steps_forecast) + ' Day Forecast'))\n",
        "  plt.xlabel('Day')\n",
        "  plt.ylabel('Daily Sample Size')\n",
        "  plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IyUp4NnzWOcs"
      },
      "outputs": [
        {
          "data": {
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bkgLPPqszLo0xxnRfa9euPdwjZUxrNPYzJCJ5zrnsEIc0qlP1kLWmOKxXM4/j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\n",
            "text/plain": [
              "<Figure size 1000x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_forecast_helper(observed_counts, forecast_samples, CI=80)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QmS-ybPM903-"
      },
      "source": [
        "## VI inference\n",
        "\n",
        "Variational inference can be problematic when inferring a full time series, like our approximate counts (as opposed to just\n",
        "the *parameters* of a time series, as in standard STS models). The standard assumption that variables have independent posteriors is quite wrong, since each timestep is correlated with its neighbors, which can lead to underestimating uncertainty. For this reason, HMC may be a better choice for approximate inference over full time series. However, VI can be quite a bit faster, and may be useful for model prototyping or in cases where its performance can be empirically shown to be 'good enough'.\n",
        "\n",
        "To fit our model with VI, we simply build and optimize a surrogate posterior:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7aZQEnTThgMT"
      },
      "outputs": [],
      "source": [
        "surrogate_posterior = tfp.experimental.vi.build_factored_surrogate_posterior(\n",
        "    event_shape=pinned_model.event_shape,\n",
        "    bijector=constraining_bijector)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "65cf0_EiimGq"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Inference ran in 11.37s.\n"
          ]
        }
      ],
      "source": [
        "# Allow external control of optimization to reduce test runtimes.\n",
        "num_variational_steps = 1000 # @param { isTemplate: true}\n",
        "num_variational_steps = int(num_variational_steps)\n",
        "\n",
        "t0 = time.time()\n",
        "losses = tfp.vi.fit_surrogate_posterior(pinned_model.unnormalized_log_prob,\n",
        "                                        surrogate_posterior,\n",
        "                                        optimizer=tf.optimizers.Adam(0.1),\n",
        "                                        num_steps=num_variational_steps)\n",
        "t1 = time.time()\n",
        "print(\"Inference ran in {:.2f}s.\".format(t1-t0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zX8WtcLmk2mj"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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vr93B7U+t6Pe2Pn5cGRNLcxiZl8lZU0ppc8jLTCMnQ+P/iQwVhb4cEPPfrWbJ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\n",
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.plot(losses)\n",
        "plt.title(\"Variational loss\")\n",
        "_ = plt.xlabel(\"Steps\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kQoUExeBkpC0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f93ff4735c0>"
            ]
          },
          "execution_count": 0,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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Bwymn5JhMfXH++UMn7WuaRiAQQEqJZVm0trYCTKoIk1KSz+dJp9MlsVV08zcM\ng0QiQSwWA8Dn8xEKhfD7/Xi93lJPy0OVYBB+8YvBqxezWfjjH93IV/9pSIVCoVAceozkm/d64I/A\nEUKIJ4Fq4NKD7SSE8AGPAd6+89wtpbxRCFEB/AZYCOwCLpNS9oxp9DOEfB7icY2qKjehfcsWk1xO\ncMIJk2/tkM1CMrnv3PsjhMA0TUzTREpJoVA4QIQFAoEDIlCPPgrf/77rrL5okes7NZjJp+M45HI5\nUqkUiUQCy7LQNA3TNAkGgwO27X8Oy7Lo7u5GSlmK0IVCIXw+H6Z5YM7cbKaYaufxDL5+wQIIBNwE\neyW8FAqF4tBGjCQBWwhhAEcCAnhVSnnQxCXhhjCCUsqkEMIEngA+CbwL6JZSfkMI8TmgXEr52eGO\ntXbtWrlhw4aDX804aG9vJ5VK4R1DQ8WvfS2MlIIvfjEOuAnUr7xictRRhUnP3fniFyOUl0uuvz4x\nqv2KIqxQKJSETzES9sQTOtdf70ZpQiG3gXMqta+tjW3bZLNZkskkyWSyJJ48Hs+YphCLY7EsCykl\nhmEQDocJBAKHxLTkq6/Cf/4n/Ou/um2CBuPLX4aODvjBD6ZyZAqFQqGYDIQQG6WUawdbd1BZIIR4\nA/iWlPJH/Zb9SUr5tuH2k66iS/Y9NftuEngHcHbf8p8DjwDDCq+ZztKlFn/7m49sFnw+ME045pjJ\nSaof7NxPPunFskaXoF0USh6PpzRFWIyEfetb9fh8JoGATjotiETcyNYtt1gsWdJBJpMpCSSv14s2\nUhv/EYwFXGEXj8cHTEuGw2F8Ph8ej2fWTUuuXw9tbVBTM/Q2K1fCL3/pitzQ8J68CoVCoZjFjOQb\nswCsE0LcJoQoTpbUj+TgQghdCPEi0A48IKV8BqiVUrYA9N0P+nUkhLhOCLFBCLGho6NjJKebNlas\n2Ofn9eqrBnff7SednhpxsGKFRS430M9rtBSFTyAQwO/3s3u3hq7nePFFiy1bbLq7M+h6hjfecLAs\nC7/fX0qSH6/oGgxd1/H5fKXx2LZNZ2cnjY2NtLS0zCp3fsuCxx6Dk05ypxOHYsUKiEahT/sqFAqF\n4hBlJN+aaSnl5cBW4HEhxAL6Eu0PhpTSllIeC8wDThRCrBrpwKSUP5ZSrpVSrq2urh7pbtPC0qUF\ndF2ybZvJE094efBBH6Y5NR5ay5e7kbXBvMTGghCCBQscdu/2YFkawaCD1wvZrMGCBRLTNKc04lTM\nUSuKvWw2y+7du+nu7p4VJrEbN0IicfDcrVWr3OT7/a0mFAqFQnFoMRLhJQCklN8EbsD19Jo3mpNI\nKWO4U4oXAG1CiDqAvvv20RxrsuhJ95AsJA++4SD4fLBokc2WLSbPP29y7LF5pio/PBKR1NfbEya8\nAI46qkB3t0406nDEETbptEY6LbjmmtSEnWOs+Hw+/H4/3d3dNDY2kk6np3tIw7J+PZSVwZo1w28n\nxIE2EwqFQqE49BiJ8PpS8YGU8iHgfOD7B9tJCFEthIj2PfYDbwK24VZIXtW32VXAvaMb8uTQmelk\nc+tm2lPtY3J8X7q0wIYNJg895OOhh7w89dQQJWyTwJVXprj00okRIJYFXV0aF12U4cgjLTo6NISA\n887LcsopM2OKr2iVoWkazc3NtLa2UhjM0GwGcMYZ8P73jyz/7rHH4CMfYdjenwqFQqGY3Qz5dSCE\nWC6l3AY0CyGO22/1n0Zw7Drg50IIHVfg3SWl/JMQ4ingrr62Q42MwJpiqvDqXrZ3bSeVT7EgugBN\njCx/6amnPPzsZ0HicYHPJ7EswU03RbjxxviUiJWjjpo4k1bDgBtucKszfT532f/+b5Cnn/YQjwsi\nkZnThqjYGDydTpNMJqmqqqKsrGxGJd+fdtrIt/V4YM8eeOMNN+dLoVAoFIcew/0O/2fgOuDbg6yT\nwDnDHVhKuQk4YIJFStkFnDuKMU4ZmqYR9UdpTbaSzCdZVrkMr3Fwe4nbbgsSCEjSaUFZmUMkIhHC\nXT5VUaLnnjPx+Rhzi6J0WvCHP/h517vSJcFV5MILMzz+uJf77/dxySWZCRjtxCGEwOfz4TgOHR0d\nxONxqqur8fsnp0fmaHj4YVi9euRu9EWx9fLLSngpFArFocqQIR0p5XV99+sGuQ0rumY7UV+UrJXl\npbaXiOfiB92+sVEnGJRUVzvU17vW5MGgpLFx6vyn7r3Xz1//6jv4hoPgOPBf/xXiwQe9NDUdOOa6\nOofjj8/z0EM+MjNLd5XQNI1gMIiUkj179tDe3j6tfSrb2tzm1w8/PPJ9ysqgvt41UlUoFArFocmQ\nwksIcYIQYk6/5x8QQtwrhPhun/v8IU3IE8Kre9nSvoWWRMuweV8NDTaplCAUkqWk+lRK0NAwdS0t\nly+3eO01g7Fojd/+1s+mTSbvf3+aJUsGH/OFF2ZIpwWPPDI2cTdVFB3zE4kEjY2NxOPxMeXsjZf1\n69370TrRr1wJW7fuc7tXKBQKxaHFcElM/w3kAYQQZwLfAH6B26fxx5M/tOnHo3uIeCPs6NnBGz1v\nYMvBRck116RIpwWJhMBxIJEQU14FuHx5gXxesHPn6Kzyn3zSw1/+4uecc7KsW3dg38kiRxxhc845\nWebMmfn90YUQ+P1+TNOkra2NpqYmcrkcjz4Kl14Ka9e6948+Ojnnl9IVXkcfDaN1QjnpJDcvLDt0\nG06FQqFQzGKGE166lLK77/HlwI+llL+TUv4bcNi4DelCp8JfQUeqgy1tW8gUDpxrO+WUPDfeGKeq\nyqGjw+2bOFWJ9UWWL7cQAl55ZeTCK5+Hu+8OsHx5gSuvPHhV5FVXpVmzZmZWDw6GrusEg0Fs2+bu\nu9v5xCcKtLVJamuhvR2uv35yxNf27bB379j6Lp50ktsXcwakqCkUCoViEhjuW1oXQhhSSgs3Gf66\nEe53SBL1RUkX0mxq28SRVUcS9UUHrD/llPy02i2EQpL58y327Bn5n8bjgS98IY7XK0fcbiidFjzx\nhIc3vSnHJJjWTwoej4c77oji9Rbo7HRwHJ1wGGzb7aF4wgl5hBClGzDg+WDLhuP1192K0NFUNPZH\nSujpgYpDfkJfoVAoDj+G+7q9A3hUCNEJZIDHAYQQS3CnGw87AmaAgl3g5faXWVi+kLmhuRNuXWA5\nFulCGr/hx9RHZ4r62c8mCAYPnhyUz8OTT3o5++wcVVWjc3/fssXk9tuDlJc7nHDC7Il+NTYamCZ0\ndOhEIjlyOQfDELz2ms7evXtHdIxirlhRfJWXlxONRg9om/TWt8I554w9anXLLW6C/f/8z9j2VygU\nCsXMZUjhJaX8mhDiIVw/rvvlvgxlDfj4VAxuKhlpArapm0R9UXb17CKZS3JExREY2tgDgLa0SRfS\nxHNxutJdpPIpJBJNaMwvm09tsHbExw+FDn4NUro2F3//u5f5822WLBldNv7atXlqa23+/Gc/a9cW\nZo3b+vz5Ns89Z+L3S8JhDSk1kkm3PVJguCaKQ+A4Dt3d3cRiMaqrqwmFQgjh5vhp2vimCo84ws0R\n6+qCysqxH0ehUCgUM49hJ4uklE9LKe+RUqb6LdsupXx+8oc2tfxt99+4e8fddGY6D7qtJjQq/BX0\nZHvY3LZ50LyvoZBSkiqkaEu28UrHKzzb9Cyb2zazJ7YHKSVRX5RyXzkhT4jGWCMvtLxAe6odRx48\nMiUl/OQnQR58cGjvsfvu8/H3v3t517vSoxZd4IqKt7wly86dBlu3zp4Z51WrCmSzGtGog+PA1q0G\nu3cbXHXV2Aogiu75hmHQ0tJCc3Mz2WyWb30LvvWt8Y115Ur3fuvW8R1HoVAoFDOPWZKlM7nk7TzP\ntD7D9th2/vOl/+SPO/84or6NZd4yJJIXW1+kO9M96DZSSjKFDB2pDrZ1buOZ5md4qfUldvTsIGfl\nSkKrzFeGR9/XZkgXOlFfFJ/h4/Xu13m+5Xm6M93DRuaEgD17dDZsGLxd0aZNJr/5TYATTsjz9reP\nvWzutNNylJU5/PnPsyMDPJ0WbN9ucP75WRoabDo6NObPt5k3z2LXrvGJR8MwCIVCWJbFtm1NPPpo\njlBofJWfixaB16v8vBQKheJQZPaELCYRj+7h02s+ze9f/T0vx17m2dZnebHjRc6sP5NT55w6QBDt\nj9/wY2omr3S8woKyBcyLzCNv50kVUnRnuunJ9GA5bmTJa3iJeCMIRj4/Z2gG5b5y8naebZ3bCJpB\nFkYXuscZZJ5vxQqLhx7yks+7yfNFslk3GjZ/vsW11ybHNUXo8cD552fZutU84DwzkWxWsHSpxcUX\nZ1iwYJ8ouv32APff72P+fJszzxzaSmMkeDwetmwJkc1aLFvWSixWRiQSOSD/ayQYBhx5pBJeCoVC\ncSgiRpLbJIRYACyVUj7Y1/DakFImJn10faxdu1Zu2LBhUs/x5NYnaY+1kyHD3xr/xvae7QCEPWE+\ncvRHCHvCw+4vkfRkezCEgS1tBAJTN/EZPnQxcQ72WStL2kpT7iunoayBkCc0YP0LL5jcemuYz38+\nzvLlA6cSt20zqKpyRp1QPxhSMmvyu4bCtuHb3w7z6qsGn/tcgqVLx+d0/9WvRkilBF/9ag+5XBbD\nMKipqRlTDtmLL7oNy9euHdeQDlscxyGVSuH3+zFGWrKrUCgUE4QQYqOUctBP8IP+HBdC/ANwN66h\nKsA84A8TNroZRm2glg8s/wAfXPlB5gbnUuOvOajoAhAIKnwVBD1Byn3lRH1RgmZwQkUXgM/wUeGr\nIFPI8FLrS2zv2j4gx+zII10/r61b3YpIx3EFF7heXxMhumCf6Ors1OjunrkK7OGHvbS1Df4213X4\nyEeSrFxpEQiM73Vpb9d47TWDU0/Noetu/pemaTQ1NbF3717y+dFZjRx7rBJdY0FKSTKZZPfu3bS0\ntNDU1DTq116hUCgmk5HMg3wUOA2IA0gpXwNqJnNQM4HFZYv5p6P/icuXXl5a1pJq4Wdbf8be1ND2\nAxMttIYiYAao8FfQm+3lhdYX2Nmzk7ydJxCQnHCCew9uO6Cvfz3Crl0TP65sFm64oYw//nFm5nrt\n2aPzi18EWb9+6GKDUEhy/fUJ6usdpGRMLZcAAgHJe96T5rTT9n3JF/O/stksu3fvprOzE9seef7X\n1q1uw2zFyMjlcuzdu5eWlhZ0XScUcqPBe/bsIataASgUihnCSIRXTkpZ+jYRQhjAYdFJTghBwNw3\nTbS+eT2vx17nvzb/F797/Xf05qbfzizkCRH1RWlPtbNx70b29O5h9Zo0v/udnzPOqOYb34iwaFGB\nhQsnvtWPzwennprj8ce99PTMvKjXXXcFCAQcLrro4F+6RZuNn/wkOKY+iaGQ5IILslRUHBg58/l8\nBAIBYrEYu3fvHnH/yB/9CH7969GP5XDDsiw6OjrYvXs3+XyeYDBYml70eDyYpsmePXtIJg9eMKNQ\nKBSTzUiE16NCiBsAvxDizcBvgf+b3GHNTN656J2cWncqmtB4oeMFbnnxFu5vvJ+sNfZf04506M31\n0phoZHPXZp7c+ySP732cnlzPiI8hEES8ESLeCH97JMsN/+Zlx26b3l4Nw5A89ZSXp56anAz4t7wl\ni20L7r9/ZjXPfvllg02bTC66KDsiU1khoKbG5umnvfzpT6O7lqYmnSee8DDcjJYQgkAgMKB/5MGi\nMEcdBa++OvYo3KGOlJLe3t6SmA0Gg3i9B0Y3DcPA5/Oxd+9eYrHY1A9UoVAo+jGSrNPPAR8CNgP/\nCPwFOCw9tQNmgAsXXshJc07igcYH2NK1hceaH2ND+wYuW3IZS6IDW1hKKUkWkvTme+nN9dKb72VZ\ndBlV/ioAHt/7OPc33j9o9OPhpof53PGfw6sPPU22P5rQeOj3ywn4JXt2GUCB+Q0xcjmd7/wwz2cX\nbEQXOrqmowkNXfTdazq60BFCoAsdQzPcdZqGEAKv7sVv+gedRq2tdTjxxDzr1/u46KJsaYpzOpES\nfvObAFVVNueeO3JR/Na3ZtmzR+d3vwswb5494r6UDz3k5YknvBx/fIGDBYOL/SPz+Tx79uzB6/UO\nWflYVeWhtzfMU0/1smjR8Oqr6KZf/JsV74uP+z8fqhWSYRizJhE9k8nQ3t5OPp/H7/cftHpU13UC\ngQDt7e1YlkVlZeWEd51QKBSKkXDQT1kppQP8pO92SOM4I0uwrvRVcsWyK9iT2MN9jffRnGym2l8N\nQMEp8LOtP6M310uikMB2Bk7xeY/wloSXV/cipSRkhoh4I5R5yijzlpEqpPBonpLosqXNix0vcnTl\n0cNaWwC0NPupqMoxf0EWr8/G9Oh4TehoCeMzfEgpkVJiS5uCLCD7hIIjndI6Rzql5f0JmAHK/eVE\nvBH8hh+v4Y7vrW/NsHGjyfbtBsceO/1thAoFWLbMYskSa1RWF0LAhz6UorVV50c/CvGlL/VSXz/8\ne8Ky4NlnPRx3XB6/f+SiszgFZtv2kO+7I47IIyW8+qrOggXDJ4gXxXvxbzjUsv7L9xceUkoqKiqI\nRqPo+tTkKo6WfD5PV1cXiUQCr9dLMBgc8b6aphEMBunu7sa2baqrq8dk96FQKBTjYUjhJYTYzDA/\n36WUqydlRNNETbCGrngXPdkeTM0k6Ake1G9rfng+1668lo5MB2XeMgAMYdCSaiFvu1+UATPgCipP\nGRFvhCpfVWn/NdVrOK76uEFbAvX/otzWvY173riHv+z+C2uq13By7ckl8bY/dfUZerpNQpF9Aiid\n0qmrz7gRq3H8yM/beVoTrTTHm5FIt32SN0q0KsrXvpmkpsLLTPDk9Xjgfe9Lj3nfT34yyX/8R5ie\nHu2gwuull0ySSY1TTx195VwxyjQU1dVQU+OwY4cXw5h8Qes4Dj09PfT29g5ogzQTsG2bWCxGd3f3\ngMT50SKEIBgMkkgksG2b2traGSsyFQrFocmQPl593l1DIqXcPeyBhZgP/AKYAzjAj6WU/ymE+DLw\nD0BH36Y3SCn/MtyxpsLHq729nWQyiaVZtCXbaE+1AxA0g6NuVr0nsQe/4afMW4apjW7fwdjRu4OH\nmh5id3zfS74kuoST55zMsugyNLFP7Ly0IcqPvr0Un98iELRJp3SyGYMPX/8ax6yNjXss/bGlTc7K\nkbfzSCQCgeGUMbeijJAZImAGRv3ajZdnnvFQVuYc4GE2WmzbtZs4GN/7Xojt2w1uvTU2ou1HS2ur\nRkWFM6UmtZZlkcvl8Pl8VFdX4/NNXf7eo4/C978PO3e6Dv4f/ajk+OOTdHR04DgOPp9vwqJUmUwG\n0zSpq6vDNKf2fapQKA5thvPxGqmB6hzgRNwI2HNSytYR7FMH1EkpnxdChIGNwDuBy4CklPLmkV7A\nVAmvVCpVSs4t2AW6M900JZrIWTm8undAheN00JJq4enWp3mp86WSG/7issV8cOUHB2z30oYo9945\nj5ZmP3X1Gd5xRdOEi67B+Mvv5/Ly5iDXfmYjaPtMZCv8FZT5yggYAXyGb9KiKKmU4DOfKWPRIpvP\nfGZi/H3vv99LV5fOe95zYATNceArX4mwZInFlVeOLcI2k8nn8+TzeaLRKBUVFZOe//Xoo3D99RAM\nQigE8bhNb6/NZz/bxhlnyEk5fzabRQjB3LlzB03MVygUirEwnPA66CeZEOJa4EvAw7gTVd8TQvy7\nlPKnw+0npWwBWvoeJ4QQW4H60Q5+ujB1k9pQLTXBGhL5BC2JFroyXQghCHvCU+bX1Z+6YB0XH3Ex\n5zecz/Mdz/NM2zMsiy4rrU8WksTzcY5Zy5QIrf1ZsDjF3x+pomlbA0cf557fciy6M920JdsAd6qn\nzFtG1Bcl5AnhM30TEhUE+NOffKTTGpdfPnFNFTo7df72Nx/19Qe2FdI0uPHG+KRWHeZycM89flas\nsDjmmKnNnyvmoSUSCRKJBJWVlWNugzQSvv991w8tFHIoFCxMs4Dfr3PHHVWsWzfyKt/R4PP5yOfz\nNDU1MXfuXPz+melJp1AoDh1G8hPyM8AaKWUXgBCiEvg7MKzw6o8QYiGwBngG14z1Y0KIDwAbgOul\nlAd8qgohrgOuA2hoaBjpqSYcIfZZNeSsHJ2ZTvbG91JwCvgNPz5j6m0UAmaA0+eezql1p+LIfTlI\nz7Q+w/qm9TSEGzhlziksiizCb/jRtakRiSuP6aWqJsdjD9Swak0MIdxek4ZmQJ+2kkiyVpZdsV2l\n537DT9QXLTUFH0tUrKtL44EHfJx6ao6GhonzLLv88jRNTTo//3mAujp7QFuhYp/KyQwEeTzw+ONe\nUiltyoUXuO9/v9+P4zh0dHQQi8WoqanB7/dPWOTScRxyuRzbtxvYtkNTk2DBAgvbNvB4oLFxcvMG\nPR4PlmXR1NTEnDlzCIcP3qlCoVAoxspIvjKagP4hhASwZ6QnEEKEgN8Bn5JSxoUQ/wV8BXfa8ivA\nt4EP7r+flPLHwI/BnWoc6fkmE6/hpT5cT12ojt5sL3uTe+nJ9qALnZAnNCDXairQhDbgnJrQ8Bpe\nGhONNCYaS8s9uodjqo7hHYvfAUA8H+fBPQ/i113h6Df8pWlAv+6nNlB70OrJwRACzji3g3vumMfr\nr4ZYuvxAw0qBKImrIpZj0ZnupDXZikSiC50ybxnl/nICngABM3DQCOPvfudGKt797syw240WXYeP\nfjTJTTdF+O53Q9x0U5yKCof2do0vfrGMf/qn5IhtJ8aCELBkicX27dNr81CsCCwKlFAoRFVVFZ4x\nJp9ZlkU2myWRSJBKpfoqKufy0ks+KisdDENnzx6d7m6NBQvsSW/GbhgGQghaW1uxLItoNDpjCgsU\nCsWhxUg+zZuBZ4QQ9+KKpXcAzwoh/hlASvmdoXYUQpi4out2KeXv+7Zv67f+J8Cfxj786UETGuX+\ncsr95WQKGdpT7bQkW3Ckg8/wodHnmcR+fkmISRVn6+at47S603ix80U2tm+kJ9dDxsqUKiyLxPNx\nnm9/fsjj/OOqf2R+eD4AL3S8QGOikWOrjqUh3HDQL6Nj1vbw0F9qefrR6kGF12AYmjGg2bcjHdJW\nmp5YD1K6SftFK4uwJ4zf9OPVvQPGsnChxZw5NpWVE9OLsj/BoOSTn0zw1a+W8dvf+ti40cumTSa5\nnODd7558sb10qcWLL3qIxwWRyPT+Btm/DVJ5eTnl5eUHrQyUUlIoFMhkMsTj8ZJ5rGma+P1+pBSE\nwwLHgWjUKd2nUgJNk3zxi2W8//1pjj568kSuruv4/X46OjqwbVt5fSkUiklhJMLrjb5bkXv77oeN\nxwv3E+t/ga39xZkQoq4v/wvgYmDLyIc78/CbfhZEFzCvbB49mR660l3Y0saWNlJKLMdC4npjOY6D\ngzOidjEwtopKj+7hxNoTObH2RMD9wsvZuQG+XFFPlHce8U4yVuaAW9bOEjL3iaDn2p6jMdHIc23P\nEfVGWV21mmOqjqE2UDvo+Q1T8t5rd1FZkxt0/UjQhIbf8OM39uXb5O08bck2mpwmAEzNJOKNuM3I\nPUHOfbM9qXl39fUOl16a5pvfDBMISGwbDENyyy1hIhHJKadMXiPmI490pzdfe83oM2mdfnw+1xMu\nFosRj8epqqoiHA4PECpSSnK5HKlUikQigdWXDGea5gH+Ww884CWT0fjUpxJs2OClsVGnocHm859P\nEIk4/OIXQW6+Ocy11yY544zJe62Lkb2enh4sy6KmpkZ5fSkUigllRFWNYzqwEKcDj+M63hfDEDcA\n7wGOxY2e7QL+sZ8QG5TpqGqcbKSUJUEmkSApPXakQyKXYG9iLxkrgyEMAp6DT7dNBi2pFl7qfInN\nXZsH9KasDdSybt46VlWuGnJfKd2pssnAkQ45O8fr2z30dPlYdXwHIW+AqC/qGrwOEhUbL9ddV05n\np0YqJWhtdYWBaUqqqhx+/OPJSf4G1xD2X/4lyrvfnTkgwX8mYNs22WwWr9dLdXU1UsrSFKLjOAgh\n8Hg8Q0bFLAs+97ky6uttPvWp5KDvmUIBHnzQx9lnZ/H7obNTo7zcmRQLjyLpdBqfz0ddXZ3y+lIo\nFKNiXHYSQoi1wBeABfSLkE2lgeqhKLxGgpSStJWmM+XmP9nSLuVkTcdYdsZ3sqlrE1u6tpC1srxr\nybs4rvo4wJ2+NDWzNLa9TT5+f3sDl1+9m+rayRELUsIPv7mMTEbnk1/YBlqenJ0rWW1oQqPMV0a5\nz80V8xv+Qc1qR8oFF1RRXe3Q2KiTSGisXFlACOjo0Ljvvs6JuqxBmUwRO1Hk83kKhUKpTZHH4xlx\ntCiZFFgWRKMH/yFoWfDFL5ZhGJKrrkoPKHiYaLLZLLquM3fuXOX1pVAoRsy47CSA23ErG/tHrhRT\ngBCCoBkkGA0yv2w+8Vyc1mQrPRk3uhIwA2NKgh/rWBaXLWZx2WLetvBtbI9tZ3FkcWn9+qb1PN/x\nPEujSzmm6hjmhY+is93LEw9Vc/F7myZlTC9tiNLS7OOS9zdimhIwB0zNOtIhXUjTk+3BDSpKgmbQ\nrVL1RUpJ/iONJDY02HR2aixcaOM4NpoGiYSY0CrKoZjpogvc6sDRJts3NurU19uEQiOPvOs6XHJJ\nmttvD/LVr0Y488wcl12WJhye+Oi9z+cjm83S1NREfX39mIsJFAqFoshIhFeHlPKPkz4SxbBoQitZ\nLuTtPLFsjL2JfVWVQU9wyqYiDc1gZcXKAcuydhZHOmzr3sa27m14DS/aqafwxAtv5uwed1poIikU\nBA/+uY66+uyQnmWD5YoV7EKpghJcMeYzfK4Y87hTlD7DN2hu3TXXpLjppgjgJtwnEoJ0WnDNNakJ\nvbbB2LNH5/vfD3HNNalxu/LPFLq7Nb72tQhnnJEbVYsnIWDt2gKrVsW4914/f/ubj+efN7nhhvhB\nWzyNhf29vqbSyV+hUBx6jER43SiE+B/gIaA0Z1SsUlRMPR7dQ02whppgDelCuiQkLMeaNof9y5de\nzlsWvIXNXZvZ1LmJ5mQzherHeKP+BT72zYuJ7HoPdfUZzrl0EwtWNlPlrxrXlOmzj1cS6za5+KN7\nRhUNMnXzAFFlORa92V460h2l7qSGZhD2hIn4IgRM12rj5JMlN94Y57bbgqXk72uuSQ2ZWO9IB9ux\nsRzLLbhwbBzpYDkWeSdP3spjaAZVgSr85vCvRXm5Q2urzvbtxiEhvKSE224L4jhw/vnZMR3D54PL\nL89w+ul5HnjAS12dK7oefdTD7beP7G80UjweD4VCoSS+AoHp7WKhUChmLyPJ8foVsBx4mX1TjVJK\neYD31mRxuOZ4jYZiQn5bso2uTBdAKXIzHUn5nZlO/vjca/zu8Z0Yz/0zK+bWkstqdFT9gYpzfkak\nrEDADFDlq6LSV0mlv5Iaf80BkbSh2LYlzPZXIrz9suZJGb8jHfJ2nrydL5nUCiEIeoKUectK9heW\nbZGzcxScAnkr7947eQp2YdjqVV3oaJqG7bgVsOX+curD9YQ94SELAm64oYzKSofrr584Z/7p4skn\nPfz4xyGuvDLFeedNXA7gww97+fjHo5SXOzQ02GSzblTyxhvjE1J5WuxjqYxWFQrFcIw3x+sYKeXR\nEzwmxQRTTCQv85VRsAvEsjE6050kC0kse2CEpOgmX3KVnwSq/FU0/fFsFrZ6ERHQdQuvz0FzgsR2\nHEnl2ldJF9I0FvaZvVb5qwYIr1+9+ivCZtgVZ/5Kqv3VVHgrEEKwfFWC5asmT4BoQjvA6BX22Vo0\nO/sEX1FE6UJ3TWx1LwFjdBGRdD7NlvYtBMwA8yLzKPeXHyCYly0r8PTTXhzHbVc0W4nFBLffHmDp\nUos3v3liCy9uvz1AWZlDIqGxbZtGJOJgmvA//xOcEOFVNFptaWnBcRzKysomYNQKheJwYiTfuk8L\nIVZKKV+Z9NEoJgRTN6kOVlMdrAbAlva+aIydJ11Ik86nSVtpkvmBJqe60DF0A1Mzxy3KWpr9VFTl\nSlOBiV4Pqa3vxHnuYo6pfIOGlU2E5u4mZnXQle3Cp+8TOelCmm3d2w44puYEEN1LuPKUk1hWtWBc\n4xsLHt0zKQUNAdN16M/bebZ3bUcXOvPK5lEdqC6db+lSi/XrfTQ16VOS0D9ZJJMaVVUOH/rQ4NYR\n46G5WeeII2yyWYfOTo3eXg3LAind93JLi4bXCxUVY88F03WdQCBAW1sbtm1TXl6ujFYVCsWIGck3\n6+nAVUKInbg5XgJ3qnHK7CQU40MXOn7Tj58D84iklO6UWt/0WMbKkMwlSRcGirKxmLnW1Wfo6TYJ\nhlyREIkWyOc1pAObnqtgw5NVeH2r+exXXsHjdd3Ki5i6yQdWfICuTBed2U46M520Zdp4badNvHcn\n6fTJpW2fbXuW13tfZ15wHvNC86gP1ePVZ+eUcVHY2dJmT2wPu2O7qQnWUBeuY/lyjdNPz6HrM6KD\n1piZN8/mppvik1KpWaw8DYdlnzi16ejQmDfPfQ/ec0+AZ57xsGCBxZo1BY47Lk9Dgz3qsRSNVjs7\nO7Ftm6qqKiW+FArFiBiJ8Lpg0kehmDaEEHgNL176CZW+1JWiKOvN9dIcbyaZTWJq5oD2PsPxjiua\n+NG3lwIQCNpkMxqGIfnw9a+x8phedr4Woq3Fh8frKq5f/mgR+YLGiqPjLD8qzrLaZRB1bSNeuHMe\nu3cF6M32cvxbn2Vl/T4RuT22nW3d23il65XSNVX5q5gXnMfS6FJWV82+3wi60CnzlSGR9GR6aE+1\nE/aEueR984j6ori/f2YXiYTgr3/18fa3Z5iswsD9K09TKbcNUbHy9OKL0yxcaPHCCyb33uvnD3/w\ns2JFgc99zp227u+X9tRTnmELKYQQBINBYrEYtm0rl3uFQjEiRuxcL4SoAUofl1LKxmE2n1BUcv30\nI6UkmU/SmmylI92BQBDyhA46HfnShij33jmPlmY/dfUZ3nFF05D2D+v/VsMrL7reXABVNTnm1Gd4\n9P5afH6Lrg4vqaRBVU2Oj3zmtdJxOjOdNCYbaUo20ZxspjXdiu24EY5Vlau4YtkVgDt9+XDTw1T4\nKgiZIUJmyPVJM4MEjMCUNzkfLVkrS7qQIRULc8ziGioDlZOWozcZ/OhHQZ57zsOXvxxn/vzJmyo9\nmGAqEo8LXnrJRNPgtNPyWBZ85jNRjjjCwuNxuPvuAKGQLAm44ZL0U6kUwWCQ2tpa5XKvUCjG7Vz/\nduDbwFygHdfBfquU8qiJHuhQKOE1s8jbebrSXTQnmsnb+Qm3sIh1m2zbEmHbljKef6YcXXcwTNj5\nWpCaOVm8PpvyigJfunnwNp8Fp0BrqpWmZBMVvgqOLD8SgNdir/HzrT8fdB8hBB9f/XFqAjWA26Oy\nI9NREmfF+7AZJmgGp03wPPtkBffeWc91NzxDWXmeueG51ARrDmpHMd28+KLJLbeEeec7M1x8cWa6\nhzMoyaTg7rv9vPCCh8ce85LPu0768+bZ+Hyub9tw7aEymQwej4e6ujoMY2YKYtu2yeVyOM74/c50\nXcfr9aoon0IxCOOtavwKcDLwoJRyjRBiHW6/RcVhikf3UBeuY05oDol8gpZEC12ZLjQ0gp7xi5Jo\nRYGTz+zi5DO7eObxEwhXFchmdEJhi/KKAghJS/PQQsPUTOaH5zM/PH/A8gpfBec1nEc8HydZSJZu\nKStFppAZIB639mxle8/2QY9/RNkRXLPyGsAVofc13kfUEyXqjVLmLSPqiRL2hCclgjZvQRohBL17\n5zJ/TjetyVaaE82lPL5ikn7RSsSjeTB1c1qjeem04Gc/CzJvns1FF81M0QUQCkmuvjrNVVelOeec\nagxD0turkc+7nmHBoKSxceholt/vJ5vN0tzcPKNaDDmOQyaTIR6Pk0pNrNmvEIJIJEIoFFIiTKEY\nISP5hixIKbuEEJoQQpNSrhdC/Mekj0wx4xFCuI7v3gg5K0dXpovmeDMFpzBhPSX7J+jPW+C6m6eS\nOnX1o/8Cr/RVcmb9mYOusx17gDg5qfYkFkUWucKskCJVSJWEWpl3n4VALBfj2dZnDzieJjQingiX\nLr2UBWG3+nJvai/JQrIk0sZSHVlbl8Xjddj1RpDVx8eIeN18JomkYBfozfbSle4qeY8VMXWToBnE\nZ/gImkE8hpvEX6xenczE8N/+1k8spvGJT/QyQwNBAxDCrSDt7NSYO3efFUsqdfD2UD6fj1wuN+0t\nhhzHIZvN0tvbSyqVQkqJYRj4/f4J/Vs7jkMikaC3t3eACPP5fKrYQKEYgpF8DMaEECHgMeB2IUQ7\nMPutsxUTitfwMjc8l7pQHb25XloSLfRke9CERsgTGrOJ6/4J+umUTjZj8I4rdk7k8NG1geM7svzI\n0hTlcATMABcuvJBYLkYsH6M310tvrpdkIUksF8Or7Zu6fqb1GTa2byw995t+FkUWcVz1cSyNLh3R\na6Tr0LAoze4dwQHLBWJYqwtb2uSsnJun57QesN5v+PGbfryGF7/hx6N79nm96QaGGLs4u+CCLAsX\n2ixePHssMPon6QcCkpYWHcOQfOYzB48Yeb3eaWkxVBRbiUSCRMItFtB1fcLFVn80TStdX1GExWIx\ndF0nHA4rEaZQDMJIcryCQAbQgCuBMuB2KWXX5A/PReV4zU6yVpaOVActyRYsx0IMU4knEGhCK31A\nFx8LBFs2VvCnuxbSujfA3PrssAn6M4WCU6A310u5t7wk6p7c+ySvxl6lN++KM8vZ9/tlcdliPrhy\nZM0g1t9Xy8N/reWGb2zB75+Y3oSWY1FwCqUWR4Nh6iZew4tP95XMZYvCrBg504Ve+htalisUZ+t3\nbjFJ/9VXDeJxjWuvTfLRj458qq5QKJDP56mvr5+0FkNDiS2PxzOtYsdxHPL5PLZtKxGmOCwZV3J9\nv4NUAmcCjVLKjQfbfiJRwmt240iHdCGNlBKJxJHOgMeO42BLGwen1M+w2OfQljZSylKvw3Shr5my\noCQAZiNSSmL5GJs7N/N8x/OcUHsCp9WdBkB3tpvXYq+xumr1oNO1nW1e2lp8LDsqjmlOnadX8W9Q\nvB9KoAXMAEFPkPvvWUCy189HP5rA7/HO+KrRoZASvv71MC0tOt/8Zgz/KGbQ+7cYCgaDJdExHvHR\nX2wlk0kcx8EwjGkXW0OxvwjrnxM2E8erUEwEYxJeQog/AZ+TUm4RQtQBzwMbgMXAT6SUt07SeA9A\nCS9FkaKIS+QSdGe6iefi7opZLMSkdAVoMTL2QOMDPNr8KIZmsKJiBWuq17CkbMmsES4Fu8Abr3v5\n2feO5PjTW3nzO91pYY/hcW08vCECRmBAntlM5/XXdb7ylbIxVWXatk02mz1AZAgh0DRtwP1gj/tv\nk8/nS2KrGNmaTQntjuOQy+WQUqJpGpFIhLKyshlTiKBQTBRjrWpcJKUs1utfAzwgpfyAECIMPAnc\nOrHDVECfaWk+j2EYyg9oEIo5YyFPiLpw3QFCLJaNuRvOIiEmhBiQ3zU/PJ8jyo5gR3wHmzs3s7lz\nM2FPmDXVaziu+jiq/FW0Nvtob/Wx+vjY9A18KBwP9/12KVVV8I6Le/F4o4AbMUsX0sSysQHJ/7rQ\nCXqC7q2vAMDUTXRNH1du2USyZInNiSfm+etffaxblyUaHXmkUdd1gsGBOXnFH7xSygMe27Y95Hoh\nxKyuHtQ0DX9fyNBxHHp7e4nFYlRWVlJWVjZrr0uhGA3DCa9Cv8fnAj8BkFImhBATk1iiGEAul6NQ\nKBAOh0kmk3g8HvVL8CAcikJseflylpcvJ5aL8WLnizzf/jzd2W4ea36M3lwvly69lOefqeDZJytZ\nuboXYwqnG0fC+r/W0tnu5eqP7Ch1JQBXYOmGfsDfwJEOBbvg5gM6LQccTwhRSvb3aB48hhslM3X3\npgvdvWkD7ydasF1ySZqurhCplEY0Or5CgYmYcpztFEWY4zh0dnYSi8Worq4eMCWrUByKDCe89ggh\nPg40AccB9wEIIfzAQdWAEGI+8AtgDuAAP5ZS/qcQogL4DbAQ2AVcJqUc3JHwMKFQKJDL5QgGg9TV\n1ZVK0pubm7Fte8qqog4FRizE+m1fTAo3dGPM1ZeTQdQb5ez6szlr7lnsTuzmhY4XOLb6WAAWLE5x\n/8ZGfvr8n1h35FEsjCyc1im7YoeCvU1+4r0mp57dwZLlyYPviPs3OKBtVT+KuYC2Y5OxMqQKKRzp\nDJljVkQXOpWBSqoCVYS94/dVq611+NKX4uM6huJAin0vLcuipaWFQCBAVVWVSvtQHLIMl+NVA/w7\nUAf8QEp5f9/ydcDxUsqbhz2wmxdWJ6V8vm96ciPwTuBqoFtK+Q0hxOeAcinlZ4c71qGa41XM/TBN\nk5qamgPKvguFAq2treTz+VJ4XjE+HOmQtbIU7AKWtMhaWfdWyJKxMhTswgH7aEIrTXvpmj4j2vQk\n4wYf+5+/EFj2NBWVeXRNZ35oPosii1gUWcT88PwpE2IvbYjyo28vxee3CARtkgmDbEYf0NZpOiiK\n7oJTQBMa1YHqCRFhiYTghRc8nHlmbgJHqyiSy+WwLIvy8nLKy8tVyoViVjKmHC8pZTvw4UGWrwfW\nH+ykUsoWoKXvcUIIsRWoB94BnN232c+BR4BhhdehRrEqSdM0amtrCYfDg4bWTdNk7ty5tLW1kUql\nCAQCKgQ/TjShuQ71Q2gSKSWWY5XsFQpOgbyVJ2NlSiItmR9ZJGckSKRraDpKM9VQxGJ57j3ku+dQ\n2fA4relWdsV3sSu+i/WsZ2l0KVetuAqgVCU6GYJRSvjNzxaQzWqkUz4CwRThiIWmSe69c960Cq9i\n9BPc16A7001bqm3cIuzRR7389rcB6upsli5VloYTjdfrxePx0NvbSzwep6qqasjPyInEsqwZ2+pJ\ncWgxJe8yIcRCYA3wDFDbJ8qQUrb0RdYG2+c64DqAhoaGqRjmpCOlJJvNIqWksrKSSCRy0F9zuq5T\nV1dHZ2cnPT09BAIBlYA6iQghSrlDfgaPMkopsaRF/2hxKQGaA5cN2Lf/eiTZQpY98T30ZHtG7fa/\nrCHAa1uv4CPvX03GSrM7sZud8Z3sjO9kUWRRabs9yT3c9sptNIQbShGxeaF54xJiHW1ennm8km1b\nyti8yY8R7MVXFiPpSeAjjD9YNWxbp6lmOBFWE6yhKlBFyBMakQh705uyPPCAjzvvDPDFL8ZnrU/Z\nTEYIgd/vx7Zt2traSvlfExn5L/atTKVSJJNJLMsiFApRVVWlcmsVk8qIfbzGfALX9f5R4GtSyt8L\nIWJSymi/9T1SyvLhjnEoTDVms1ls2yYajVJeXj6mX1axWIz29nb8fr8Kvx9CSClJ5BM0x5vpyfZg\namZJJAxHMm7g8dl4PIMIvL4KOIBn257ljzv+OGC9oRklIXbG3DNKIqzgFEgX0qStfrdCmlg6g7fj\nRFYuKKdmTo7/2/gydz73NL5ojO6Yg5SUkvyF1Kh/6ldUVFh86eYt3PPGPWTtrGsl0e8W9oSJeqOE\nzINf62TRfzpSFzo1wRoqA5UHFWGPPurlpz8N8rGPJTjhhAOnpxUTSzEPNhKJUFlZOSZhVKwYz2Qy\nJJNJstks4OaYmaaJrutks1kcx1FVlopxM64m2UKICill9xhPbAK/w3W6/33f4jYhRF1ftKsOaB/L\nsWcL+XyefD5POBymsrJyXL3botEopmnS0tKCaZrqV9khQqnnZXWEdCHN3sRe2lPtB2239Mb2EPfe\nOY+WZj919ZkBjv79p2VOrD2RoyqOYld8Vyki1pZuY0fvDtoz7ZS3vJM//mY+e1t0us99L3PmZomU\nFSgUBMmESSJukEkZ1O5ZzcUnRjn3rW1Uz02x4OidaBqEoz52b61Dywbw6DqFgk4uY/KOK3YBsD22\nnUQ+Meg1nDb3NN6y4C0ANCWb+OvuvxI2w1T7q6kL1lEXrCPqiU5ey5v9ImGd6U5aki0HFWGnn57j\nvvt8/Pa3AdasmR09KGczpmliGAbpdJpEIkFlZSXRaPSgwqgo2JLJJKlUCsdx0DRtyL6VPp+vVGXZ\n29tLbW2tyq9VTDgjaRn0GvAicBvwVznCEJlw39E/x02k/1S/5d8Cuvol11dIKf91uGPNxohX0bHa\n5/NRVVU1of+8xYpHQFU8HqLkrBztqXaa481IJCFPaMDUYDGhPZ/TMD0O/oBFNmPw4etHltCeLCTZ\nFd/FK1sN1v/g/aXE+K3L/hFp+Vh9lEPj9lrIRYj6fTTUa5x+5BEcv6wSTaOU8xYwA3g0D5s2lg8p\nAnfGd5LIJ0pNxvvf1tas5cTaEwHY3LmZ37z2mwPG6jf91AXquGLpFW5+3hQwVCQs7NmXa/TiiyaP\nP+7lmmtShEIzy9LjUKZ/jmx1dTWhUKj0NykatBYFmmVZpQbhpmmOKoJVbPlUVlZGRUWFyv9SjIpx\ntQzqE1BvAj4InIhrBfEzKeX2g+x3OvA4sBnXTgLgBtw8r7uABqARuPRgEbXZJLwcxyGTyWAYxqR6\n0hQrHnO53KT1gVNMP5Zj0ZXuYk98D3k7T8AI4DW8/Pu/rKKn2yTW7SWd0gmFLfI5DX/A5r/ufBZd\nhxeeLeeNVwdO4+m65OL3NgHw7JMV/M+tS8ikdUyPQzploOkOtXVZyisKXHZVI1W1Wapq8lNyrelC\nmtZ0K/F8nPZMO3tTe9mb2ku6kMaje/jiCV8sRZ5ue+U2Ck6BucG5pchYrb/2gGbnE8FgIqyYE6aK\nXaaP/j9uI5EIiUSCTMbtKqBpGh6PZ9wpGcW8XIDq6uopSfJXHBqMa6qxL8L1APBAn5XEr4CPCCFe\nwm0p9NQQ+z0BQ3ZFPndEI58lFHuROY6DEILq6moikcik5gcUKx7b29tJJpOq4vEQxdAMakO1VAer\niWVj7OndQ3emm+YmL1XVBRyn0FdRaCAlpDoMkAKQdHd42PXGQOFlGPsMTbvavXS2e/F4HSxb4A/Y\nhCJu5Kul2c/yo6fWsypgBlhctnjAMikl8Xyc7lx3SXQ50mF3YjeWY9GYaCxtq2s6tf5aTp97Oqur\nVk/YuPpPR9rSLk1HGppBdaAaq3cO3W0RTjpJ5XpNJYZhYBgG+Xyezs5ODMOY8M/B/ZP8e3t7qa6u\nVjMNinExkhyvSuB9wPuBNuDjwB+BY4HfAouG3PkQxrZt8vl8qedYKBQiFArh8/mmLCFT13XmzJlD\nV1cX3d3dM7biMZfLYduu03fxw3ImjnMmowmNCn8F5b5yEvkE9fNydHQKgqEsRyxzv/BTSZ3yigK6\n4Uaxz31rG+e+tW3IY77l4haee7KSnm6TYGifE3sqqVNXP7p+hJOFEIIybxll3rLSMk1ofOa4z9CS\nailFxVrSLXRlutib2osl91k8bOvZxob2DRwROYLFZYup8deM64tZF/oBIuzuX4d5Y6uPG2v3snBu\nhJCpImFTyXjyZkdKse1TPp9nz549RKNRKioqVJGTYkyMZNL6KeCXwDullE39lm8QQvxocoY1MykU\nChQK7pecYRhEo1GCwSBer3faPmiFEFRVVWEYBh0dHXi93hmVi1DMxaivr6dQKJBKpUin0ziOG3kZ\nS+7F4UwxEf8TH9a58cshCpkcjjdNJm2Qz2pc9U+NBz9IP95xRRM/+vZSAAJBm3RKJ5sxeMcVOydj\n+BNG0AyyJLqEJdElpWVZK0tLuoVqf3Vp2as9r7KtexvburcBEPKEWBxZzBFlrhAr9w5bUD0sRRF2\n0Tt7ufXlOfzuHg/nXbIZUzOpCdZQEahQImwInnrKw223BWls1GlosLnmmhSnnDI1U9rjodjGLR6P\nk0gkDsgxUyhGwohyvEaaUD9ZTFeOl5RygNgq5hL4/f4p+ZU1WlKpFC0tLRiGMSPGl06n8fl8zJkz\nZ4AYLL6u2WyWdDpNKpUqeV7puq6E2AgpfnntbtSYW5/hwst2Mf+oHSUrCb/hH5Exa7Hdz2CJ8bOd\nWC7GG71v8EbvG+yI7xhgfjs3NJePHP0RwH1PpqzUmK0t/nR3Pc88UcknPv8qFTVp0vk0lrQGiDCf\n4ZsxTb+nk6ee8nDTTRECAUkwKEmlBOm04MYb47NCfBWxbZtMJkMwGKS6unpGfOYqZg5jSq4XQvwf\nMKTgklK+fWKGd3CmUniZpkk+n8e2bYQQBINBwuEwPp9vRkWShiKXy7F3716klNOWhyClJJ1OEwqF\nqK2tPaiIKgqxfD5fiohZljtdVBRiKqQ/MqSUpAopErkEHekOkvkkAoGhGfhN/4zqRTnVSClpz7Sz\no3cHb8TfoD5Yz7p56wBoT7fz3Ze+S22gthQNWxRZhFcfWbFNMqHznX9fwRHLklz5D7tKy21pl0SY\n6Et59RpefIavZJjrNbwYmoGpmRi6cciLs+uuK6ezUyMQkOTzAr9fkkgIqqocfvzj2de2t9jiqKKi\ngvLycvWjUQGMPbl+2F6MhyLFnK1wOEwoFMLr9c66fyKv18v8+fNpaWkhnU4P6lUzmTiOQzqdpry8\nnKqqqhGdWwiBx+PB4/EQCoVcZ3jLIp/Pk06nSSaT5HI5pJQzbip1piGEGNAkvGAXSOaTxLIxOtOd\nbt9CtNKX/1iRSGzHxnIsbGljOzaOdAbdVhNaKTG++FggEEK4j4v3Q9biTAxCCGoDtdQGajml7pQB\n6zqznRiaQVu6jbZ0G39v+Tua0JgXmsfy8uWcNOekYUVYKGyz7oI2kgkDx4Hix4YudMLe8IBtLcci\nb+VJF9JYtjWgm0ERr+EtibJDTZw1NupUVzvs3q3T26thGBCJOHR1aeTzMNsCR16vF9M06enpIR6P\nU1NTQzAYnO5hKWYwk+5cPxFMRcSrKLo8Hs+s/UDrj+M4dHV10dPTU/pgmIpzptNpqquriUYn1vSy\naITY3t5eiuYdCn+nqURKScbKkMgl6Ex3Es/FkUhMzXSnwfp8woq9KocTVEIIvLor3ooizmt4SxE1\nKSUODrZtY8t9As1yLGzHHvTxgBZMyFG3UBovBafAnsSe0rRkU7LJ/UzQPXx+7edLTcczVmbSx1V8\nbSxpDSnO/IYfv9l3M/ylVlcezYOhzVxhVox49fRoSOn2++zudgXYr3/dxYoVFj09Ak2DsrKZ//3U\nH8uyyGazhMNh1XroMGesU413SSkvE0JsZpApRynlxNVrH4SpEF6HKplMhra2NizLmtSKy+IHTl1d\nHeFw+OA7jBHbtunq6iIWi82a6d+ZiuVYpPIpYtkYHekOCnZfLmPfNJjX8Lo33Tsg0mLoxqRMWUop\nkciSb1ZjbyO9uV5XYEyhACuSsTIl89eT5pwEuOLs6xu+Tm2gllUVq1hVuWpAxSXA69tCCAFHHDlx\nzdT3pxhxLDiFUuRxf4rRMp/hw2/63b+jbmJqJh59+n5gDpbjlUoJrroqxWWXZTAMuPNOP/fd5+eI\nIyzWrMmzZk2euXOdWdMXU7UeUoxVeBXb+iwYbL2UcvcEjnFYlPAaH47j0NPTQ3d3N6ZpTngSaLEA\nYe7cuVNm5ppMJlX0a4KxpT2jcsCKPSx3x3YTz8enTYD1pynZxE9f+Sl5e18SeEO4gVWVqziq8ijC\nRhnf+/qROI7gE59/tWTtMR3Y0qZgF0oRzP5oQiPqi1LhryDgCeA3/CNqED4R9PQI1q/3ct99/iGr\nGpubNTZs8PDCCx527nR/XC1aZHHjjQObks/k6siimbZpmqr10GHIuJzrZwJKeE0Mxam6bDaL3++f\nkF9hxdyr+vr6SWswPhSWZdHZ2Uk8HlfRr0OY/gIskU9M+RTk/uTtPNtj29nStYVtPdtKokYIwT+v\n+WfaXmvgVz9exEWXNnPSGV3TNs7hcKRDzs6Rs3JIJALXpqTCX0HIE8Jv+ge0qJpIbr89wEMPebnl\nltiIphK7uwUvveQhkxFceKHrIv/Vr0ZIpeDJJ71UVDiEwzO3OrKYJlFWVkZlZaX6nDpMGG+T7JOB\n7wErAA+gAykpZWRCR6mYdLxeL/PmzaO3t5fOzk40TRtX5WM2m0XXdebOnTstuQyGYTBnzhxCoRDt\n7e0UCgUV/ToEKXqXrapZVRJg3ZluAmZgXAUCY8Wje1hV6U4z5u08r/a8yubuzcRzccq95USPSrBw\nSYqfb/wzhYUax9auLJmuzhQ0oR0QQcxaWXbFdpWEWMAMUO4vJ+KNuD05R2BNcjCSScEjj3g5+eT8\niPO3Kiok69blSs/zeaipsfnJT4Kk04J4XKOqymHOHNcE+LbbgjNKeBUbfKdSKZLJ5JS1HnIcByml\nqgifgYzEx2sDcAWuS/1a4APAEinlFyZ/eC4q4jXxFAoFOjo6SCaT+P3+Uf9zFj266urqZsQ/dv/o\n11iuRzF7GDAFmYtPmwAbbFzFL9PNrye56ZEfUlWdo7o2T32wnjJvGWFPmIgZ4ZiqY0q5YZZjoQt9\nxv1gKNgFcnauFNEzdZMKfwVRX7SUOzbaMf/hD37uucfP//t/vdTX2wffYRjOP7+KYFDS06PR3a2x\nYIFNWZlDR4fGffd1juvYk0Vx+tHn801K6yHbtslmsySTSZLJZKkSPBQK4ff7p9Xs+3BjXBEvACnl\n60IIXUppA7cJIf4+oSNUTDmmaVJXV0cymaSjo4N8Pj+iaFHRoyscDlNTUzNjkkaHin4pDj36R8Di\nuTiNvY3TGgHrP64iRy7ysO6F95IIPE1GbKYp2URTcl/jjyPKjigJrz/v+jMvdLxAyAwR8UQIedz7\nsBmm2l/NyoqVU34tQKlKsogtbboz3bQl3TZUQgiCZrBkX+IzfaVCjME+R7JZeOABL8cemx+36AJY\nsMCms1OjocGmutop+YFFIg5tbRq1tYPbm0wnmqZNeOuhQqFAJpMhHo+TzWaRUmIYRklk2bZNd3c3\njuOgaRqBQIBwODxl1e6KAxmJ8EoLITzAi0KIbwItgDIpOQQQQhAOh/H7/XR2dpJIJIb1ySraRVRU\nVFBZWTkjfzkV+2Wq6NehjxCCMl8Zq7yuANvdu5uebE8pGjOdeHQPH710Hi9tuJbf31XO3ngb0blt\nHLfuDSobWga0KsraWSzHIpaLEcvFBhxnYWQhKytW8tKGKH+4s45NtTdRqc/jvBOredMJ1US90Sm7\nJl3oBM0g9H1XSyQFu0BnupPWZGtpu2JT8aAnSNgbxqu7lbF79vixbcHb3padkPFcc02Km25yM16C\nQVd0pVKCqirJF75QxlvfmuWtb83MSF+w8bQeklKWPA57e3tLnVU8Hs+gvo3F/rjgfoYXI2JCCAzD\nIBQKEQwG8Xg86rNyihjJVOMC3ObYHuDTQBnwQynl65M/PBc11Tg1pNNp2trasG37gH/gYnuM6upq\nysvH3t9uqpBSliofhRAq+nUYIKUsCbBkPlnytip+xhXtKg543G9Z8Xn/z0VNaPhN/6gNXl/aEOVH\nNy+lYAnKKwpYFmQzBh++/rUDWjLl7TzxfJxEIUEinyBRSBDPuzlj/qYL+NG3lyKqttG++t+wbYFj\nCxYckWJBrdt7clFkEUeWHzntVZ/gvn55K0/BKZSmKSUSQxh4KaM87CfkCeE1vHh0z7jMYAeraly+\nvMCddwZ4+mkvtbU2739/mqOPLkzkJU4oI2k9VBRMqVSKRCKBbdtomlbKHxvPufP5fKl3rt/vL3Vq\nOVQ8LaeLcVc1CiGqAaSUHRM8thGhhNfUYdt2yXqiGIq2LItcLsecOXMm1aNrMrAsi46ODhKJhIp+\nHSYUBVhjbyMFp+C65CPQtH2O+QIxrIN+/8eZQoaujFudWPQ4Gwn//i+r6Orw0NIcwPQ4+P02+ZyG\nP2jxvV9uwOORbHmhjNdfPfB/6h2XNyEEvPhclP+6eSmZlIHps/DXvYFTvYmY51Vk5cscsaq9tM/H\nj/k4tYFaAFpSLYTMEGHPzPh/jfcaBMN5Ck6egl3AlgOnGoVw21rpQt/nF6e5N13TXR85zUDTNDTc\n7geaprm5cQgM3SgZ3BZ5+WWDX/wiSGurPiE5ZZPN/q2HimIrkUiU+tnquo7H45mUFI9ix5BiBK04\nLRoKhQgEAkqEjZIx5XgJ91W+EfgYIABNCGEB35NS/vukjFQx7ei6TlVVFaFQiLa2NpLJJLquM2/e\nvFnpQ7N/7pemaQfYXkgpSxVAxVv/50NRjKSpD6SZRXEK8mjf0RN2TMux6M320pZqozvbjYZ20Eq/\nlmY/FVU5ap0sHe1ekgkDKSGR8OHYApB0tPl4dcsgBeKXu3ftLT7aW314PA7ZrJfe7pVEy5eyaG6G\nrpdMPvyee9kZ30lzspkaf01p93t33EtTsokqf1Wp7+SiyKIxNwEfD1LCbd8/gjn1GS6/unFI4WpL\nu/S/l5XZkpmulO79UC2pihTbMwU9bt7ZgqUebvz3DNteDpRE19atBsuWWczE31/9Ww/FYrFSFMo0\nzSlp/SaEwDTNUt5XMbUkHo/j9XqpqalRMwcTxHAxyk8BpwEnSCl3AgghFgP/JYT4tJTylikYn2Ka\n8Pl8zJ8/vxQpmmjT1amkmMvm8/no6OgglUqVPsSklO4vZ11H13UMw/1VXbwvLheiL2LSdw/Q29tL\nT09Pqc/kdFCMRuq6riqWJhFDM6gMVFIZqCRn5YhlY7QkW+jJ9qAJjaAZPMD3qq4+Q0+3SVl5nrJy\n194gldQpryjg87tfqusuaGPdBW1Dnve8t7fy9GNV9HSb+AMOXe1ehJCkUzpz63PUB+cxLzRvwD5S\nSgJmAFM36cx00pnp5NnWZwGoCdSwrn4dR1dNnCg9GNu2ROho83LWeUNfJ7jCaTztOh3pkLWyJPNJ\nmp1moG+Ks8bglY4Q2d5ybv5/S5k/z+bqq9KsWD7z/leKye/FRPjpHovX68Xr9ZLP52lsbCwVAygv\nsvExnHP9C8CbpZSd+y2vBu6XUq4Z9sBC/BR4G9AupVzVt+zLwD8AxSnLG6SUfznYINVUo2KiKIbT\n+wup8YiVbDZLe3s7uVxuwkxpR0KxbNw0TSorK0u5H5PRmUAxNMVpyNZkK3k7j6mZBMwAmtDcHK9v\nL8XntwgEbdIpfcgcr+EY6jhvu6SZpt0BLrqsibnzDkxYtx2bplQTO+M72dG7g8ZEI5ZjcdnSy1hd\n5XZ829azjW0921gYXsjCyMIJT9aXEn58yxIScZNP/9vWaYk0OdIhb+cp2BZbN0d44J5FxGMejj2p\nk7dd3MneHbX84Y569jb5WLDA5oPXZGaUD9hMQUpJNptFCEFVVdWUeJHNZsbaMmhLUTCNZl2/bc4E\nksAv9hNeSSnlzaMYvxJeihmNlJJ4PE5nZ6fbPHoSI0/FvA9N06isrCQcDpfEXjabpaOjg0wmo/LZ\nphgpJclCks5UJ22pNhzp4NW9vPbSXO69cx4tzX7q6jO844qmUYmuIi9tiB5wHI/X4Q93zCOdMjj5\nzE7OvbC1FEkbDMuxaEo2UeOvIWC6rb3ueeMeNrZvLG0T9UZZGFnIosgiFkYWUumrHPVY+7Pr9SD/\n890jeNslzZx85sxw8c/nNNbfV8sT66vIZqG3x4PXX8AfsMikdfJZD5/67B7OOoNShexUtVOaDRR/\n9Pl8Pmpqaqa8Y8lsYazC63kp5XGjXbffdguBPynhpTgc6G/iOtEeOVJKcrkcjuNQXl5ONBodVFhJ\nKUkkEnR2duI4zpTkhigG4kiHeC5OW7KN7kw34Cblm7pZStifKDIZjQf+r47nnqwkFLa46NImVh4T\nH/H+LakWXu99nV3xXexO7CZr7YucNYQbuG7VdaVr6sh0UOOvGdX76e5fzue1rWGu//JWPJ6Z1Z6u\nrcXLN75wFCAJhmzyeQ2PxyGV1AhHs/zz/3u6tG3IE6LM5xrgFhuOH+7/V/l8nnw+XyoGUD/0BjJW\nA9VjhBCD/QcLYDwZdh8TQnwA2ABcL6XsGWwjIcR1wHUADQ0N4zidQjE1FBP5y8rKaGtrI5VKTcj0\nY7HaqaysjPLy8mEFnRCCSCRCMBikp6eHnp4edF1XSbFTSLEBddQXpeAU6M320p5qJ11IYznWsAUb\nRQQCXdNL1ZXFSj5d0wdEX/x+h7df1sxxJ3Xzx7vmkUyOLvemLlhHXbCOM+aegSMdWtOt7IrvYldi\nF/OC+3LHWtOt/HDTD/GbfhaFF7EgssC1ujD8+HU/1f5qdO3AL96L39NER5t3xokugNq6HNmMTkVV\njmTCoHl3gGhlnsrqHB0tYaK+aGnbvJ2nNdFKs3RzxzShEfFGiPqiBD1BfIZvQloqzSaKXmSxWIx4\nPE5NTQ3BYPCwF6QjYVKbZA8S8aoFOgEJfAWok1J+8GDHUREvxWzDcZxST8yxCp9CoUA+nycYDFJZ\nWTmmkH4+n6ezs5NkMjnjG4kXS9mL1aSHar6alBJb2jjSwXZsHBwcx9m3TNpYtlXywSrY7r3lWGSt\nLLa0EQi8hmtMWhRijgNCuLeNT1XQ3eXh7PPbMM3xf8Zvj23nnjfuIZFPDLr+82s/75qrAne9dhct\n6Rb8ur/UD7J4mxucy/Ly5YCbg9aZ7SxZewAlWw+BIGSGSgULeTuP5VilL/UBth9og4q+kfDv/7KK\nnm4Tn9+ho81Hb7eJBBYsTnHzT15gKA0hkeSsfU3GJRJTN4l6oyXTWI/hwaN5MLSx+5TNFopFPsFg\nkKqqqkPy/3a0jLtl0EQhpSyVtQghfgL8aSrPr1BMFZqmUV5eTigUKvXEHKnwKX6Ieb1e6uvrCQQC\nYx6Hx+Nh7ty5pNNp2tvbJywKNxFIKSkUCliWa7Lp8XioqKggEAggpZxx450ohBAYou99MEq9IKUs\nVe7FsjF6Mj0lTyyP7sFreNHRaWn28/RjlWzaGOWt725m+arBBdNIWRZdxr8e96/05HrYGd/JnuQe\nkoUkGStDxsoMsIjoynaxt7eLxp0B6uZlCAT2+WcdW31sSXh1Zbv43kvfG/Kc/7jqH5kfng/AfY33\nlSoz98dn+PjC2i+UxE3GyozYSPYdVzTxo28vBSxq6zJ4vDbte33k8xp3/7KBSz/QOOh+AnGAp5st\nbRL5BJ3pA/tE+gwfATPg3jyBkiDzGB63mnOWU3THz2az7N69m8rKSqLR6CH1fzuRTKnwEkLUSSlb\n+p5eDGyZyvMrFFNNsSdmKpUq9cQcKu+q2EC3v/fYRP1SDgQCNDQ0EI/H6erqMwOdBg8yx3EGiK1g\nMEhFRQV+v/+AKdR58+aVoobF3nOHO0II/KYfv+mnOlhdEmKpQoqebA+xTIyCU+D0t8VYdFQFD/x+\nCb/68SJWru5lwREpHvrznDEn+gshqPBVUOGr4Pia44fc7n1Hvo8/3hvG2W5y2bqX0f1JMoUMGTvD\nnMCc0na2tKkOVJemXh3plLoGSOSAKJapmfhNf2ld//vFkcWl93HezvONjd+gwlfBosgiFkcWszCy\ncEj/smPWxvjw9a8NKFy47lOvk83oBIKuYHQcsG1x0MihLvRSZG9/LMciVUjRm+09wDzW0A0ChivK\nivljHsNDwJh9pqU+nw/Hceju7i5NP47nh+OhyqRNNQoh7gDOBqpwWw7d2Pf8WNypxl3AP/YTYkOi\nphoVhwK2bROLxeju7h4gJIpl2gAVFRWUlZVN6i9Fy7Lo7u6mt7d3Sqbz+rcl0TSNUChU6qk5koTc\nfD5Pe3s76XSaQCCgfkUPQ1GIZawM3ZluOpMxnny4mr/ctYRkr4/yisK4rC1GQjKhc/OXV3LM8T1c\n/N6mg+8wgexN7eUnL/+Egj2wRVBNoIbFkcWcNve0AX0yR8LTj1Xy90eqedslzSxbOb7I4WDY0sZ2\nbApOoTRuicRreJkXnkeFv2JAs/LZQjFyHw6HqaysPOwaco+7ZdB0o4SX4lAil8uVbB80TRtQqTiV\nOVjZbJbOzk7S6fSE539ZlkU+73oh6bpeSvgfq9VGsVqz2H1AFQuMDCklOTvHtR+qpLsHTH+GeK+J\nP1Agn9OpqCzwpZu3TOh01wN/msNjD9TwiRtepbo2N2HHHSlD+ZcBXH/c9SXhtblrMxoaiyKLSvYa\ng7HjtSB//M08Otu9rDyml7e+ay9l5ZPf+7FgF0gVUgBUB6upDdUSMicuCj4V9K/GrqioKDXjnk3X\nMFZmTI6XQqGglLuVTCbJZDJEo9FpSUb1+XylcRSnQScCKSU+n4/q6urSFOJ4P2iL1Zp+v79ULOD1\nemd0scBMQAg3F6mzzU91tYPjeGlsM4jrkoaFGTr2esla2QERIkMz8OgeTN0ctfVFPqfxzONVrFjd\nOy2iC0DXdBaEF7AgvICz688u+Zc1p5oHRLsebnqYjrTr5V0bqGVhZCFzg3OpC9ZR668tTXUuXpri\nY5/dzhMPV/PI/bW8vjXMRZc1s+bEQQvyJwxTN4nqUSSSnkwP7al2/Iaf+kg95f7yA3pTzkSKbdUc\nx6Gnp4euri5M06SsrIxAIHDYiLD9UREvhUJRMmadCDwez6QKIiklqVSK9vb2ksg7HD+8R8N115XT\n2akRDkvSacGOHQaFAqxeXeBXv+rGcixydo6slSWRS5DIJ0jlUwOsL7yGt9SseiikhNe3hQlHCsyp\nn5j302QgpeSR5kfYEd/BnsSeUkSsyLp56zh3/rkAxPNxYrkYcwJzSMVC/Pl3czl1XQeLl6aQkiEr\nHyeDvJ0nXUgDMCc0h+pgNUFzdlk49E89OJRFmJpqVCgUhxy2bdPV1UUsFpvxVhnTzVNPebjppgiB\ngCQYlMRigp07DY480uKrX+1lxQrrgH2klOTtfClnLJFLEM/HyVv7IqP7W1rMRgpOgT2JPTQlm9ib\n2ktLuoXzG85nZcVKAJ5qeYo/7/ozQggqfZXUBeuoD9ZTF6xjy/o12Kkyznv7Xt54NTzuLgWDdSgY\n7BgSSSqfouAUCJpB6iP1RH3RYUXxTGQwEVacjpztKOGlUCgOWTKZDG1tbViWpZz6h+GppzzcdluQ\nxkadhgabd787zSOP+DjrrBwXXDDy6FQxOpbOp+nJ9NCT7cGRDi8/X0VXS5QL3t6JZ+bPgo2Yje0b\n+XvL3+nIdODIgS2Z4u2VlK3/KZmUTnurj8ARzxPRKsnHasllzFEVL4y1t2fezpMqpNDQqA3VUhuq\nHTZnbabS38fPMIxZL8KU8FIoFIc0xRL2np6eQ9Z4dTLI5aDo0hGPCyKR0X8fSClJ5TN84YYotpbh\nyk88h1u47vpXeQ3vhLZJmi4KToH2dHspKtaSaiFoBjmv7EN89sNr6IlJCu+8Al+ggC79yJ4FGMkG\nTl0TJCznEqUBAx9nvrmNSJnFjteCvPJStHT8P989l3TaYO78NLruvn6ppE55hVsAcTAc6ZDKp7Ck\nRdgTZm54LmW+slkXBYPRi7CijimaLw/2vP8y0zQnPUKukusVCsUhjaZpVFVVEQqFhjVedRzngA/j\n/ZftHzEr5pEdir3oiqJr716Nr3yljLe+NcNb35odVd6SEIKtm8qIdYb4yEfgxHknkbbSJHNJujPd\n9OZ63S89AT59oOnobMLUTOpD9dSH6vdbk8Pnt5lT2cne7pUIcyeON06h7FXi5us8EXcLFxY0f5yy\n5AmcdEYnu7U3eLbJZsvmY/Hm6tAwaNnrx+OxcRyBrkt6Yx4M3aGleWRmsJrQCHvDAGStLNu6tqGh\nETADlPvLiXgj+A0/XmPm++EVDVnBFWFdXV10dnZimiaappX+bx3HjUD2F1XAsFFv27apqamhvHx0\ntiITiRJeCoXikMHn8zF//nxisVjJKBYoCSohBLquo+s6hmGgaRqGYaDrOpqmle6FEKX7ov1HLpc7\nZKcya2ocVq/O89vfBkgkNK64Ij1i8SUl/OUvfmprbdauzSOEIGgGCZpBakO1ONIhXUiTzLtCLJaN\nAe6Xo1f3DmllMZrXWdf0aY2q1dVn6OmOsjr2GYiBZfQSc5rx1OzkrDOepS3TxuXvyVDpexmAe954\nni2+jXABFIRGlb+K6tpjsDsXkZcLMZOr6O70kE7qVNXmSMQNwpED8/CGor+rft7O05ZsoznevK+1\nkS9K1Luvz+RMztHrL8Js20ZKWfpfBUr/1yMlk8lMyjhHgxJeCoXikEIIQXl5OeFwuCS4iiJqLKLJ\n4/EQCARKTccPxalMw4APfzhFOCy57z4f8bjgQx9KMZLZmK1bDXbsMLj66hSDBQU1oRHyhAh5QswJ\nzXGnxAopkrkkPdmeAyoK949elO45cBq0uCxdSJfyr4p2GFPZtHpf6yEIBG1ysQpEpoYPvS/EMUvm\nH7B9Q7iBjJ2hNdVKT66H9nQ7/hWPsPuN58ikVrI4sYrq2iwdePFGO7n1q8t589taOPH0LkbrH7z/\na2FLm3g2TmdqX2ujiDdC1B8l7AnjN/0z1qriUIk6qxwvhUKhGCHZbJaOjg6y2ewhOf0oJfzxjz5+\n//sA731vmvPPP3jS/d69Gn/7m48rr0wzXXq0aBSbKWSI5+LEsrGS7QK41ZcefXL7Io60InF/8nae\n9kw7bek2NmxNsPWJFeS2vI26+gynX/I0f8t9i0zj0dg7zuST769k2eKJv4ac5VqJFIWs1/BS7iun\nzFdWmp6cyVGx0ZDJZKioqJj0qUaVXK9QKBQTRNFFv6PDNd88FH3EXnzRZNWqwogiXjMVW9puj8hC\nhlg2RiwXKxnFGsIoibGZzPMdz3PvjnuxHZtMRicQcFgUWUQ4djLnrFpMZWRy8uUsxyJrZQdEI72G\nl6AZJOwN4zf8eAw3kjZTo2NDoYTXCFHCS6FQzDT697z0eDyHZC+6eFzw858Hed/7UpSXH/hd8eCD\nXpYvt5g3zx5k75lF0Zes6EkWy8VI5pJIJAKBqZv4DN+kRsXGQsbK8GrPq2zu2szrva+Tyzu8sT2E\nV0b456M/z5oTY1Ni4mo5VqmfZH9bDV3oBD1Bgp4gIU/IbfLdN705E3+QKOE1QpTwUigUM5VMJkN7\nezv5fH7QSsqJQEpJoeBGa6Yyv+y11wy+9a0w4bDDZz6TYM6cfV+4bW0an/1slAsvzHDZZdOfsDwW\nHOmQtbKk8il6c730ZHooOAUEAq/hxWf4ZpQVRsbK8Er3Kzy1cxuNmxbj2fyPLFyS4rx3vc5jqdtZ\nVbGKI8uPxG+MrBJyInCkQ8EuUHAKB+TrBcxASZD5DF+pFZUhjGkTZUp4jRAlvBQKxUzGcRx6e3vp\n6uqakCbejuNgWRaW5X6RCSHw+/04jkM6ncbr9U5ZhG3HDp3vfCeMEHD99QkWLnSjWz/7WYAnnvDy\nrW/FBo2GzUaklGStbKkCs2gOKxADKgVnAo4jef7pSv72xzq6gn/He8630DW3uGBJdAlHVx7Nosgi\nIp7ItI2xKMjy9sA+sJrQ8Jt+V5iZbmWlqZulqcvJFGVKeI0QJbwUCsVsoFAojKmJt+M4FAqFAeXy\ngUCAYDCI1+st9bGTUpLJZEpNzacqwb+lReNb34qQSgne/OYsf/6zj6ef9jJ/vsVNN8U55ZSJabA+\n05BSljzJujJdxLNxHBw0XOEwE3LEUkmd7a9L8nOeYnPXZra2NpEvCNr2+shldEJ6Of9y/KdZc0Ic\ncKNmI4mIjbVYYCRIJAXbjZAV7MIBFas+w0fADLg3T4AXnyvj17+soHmPh4YGm2uuSY35PaeE1whR\nwkuhUMwm0uk0bW1t2LaNz+cb1Mi1KLTANYANBoP4/X58Ph+mOfyv/mKCf2dnJ47jDHqOiaa7W/DV\nr0bYvNkkmxX09mosWGBRKAhuvPHQFV/9KVphxHNxutPdJPNujpghjFLUZjp5bWuYW26uZq/2PN4j\n/o4sfwORqqXiuW/x4etfY/XxPXxtw9dcM9igawZb7D0Z9oRLxxlr+6KJophPZtkWmzaW8/P/XI3X\nb+EPWOSyHvIZk09/rokzTnNK+WQjjZTNBOE1i2tWFAqFYmYSCARYsGBByci1GJWybbtk4lqMaBUT\n80czvSKEIBKJEAwGicfjdHV1IYSY1ArLigpJMqkRDks0DQzDoaJCkkjAbbcFDwvhpQmNsCdM2BOm\nPlyP5VikC2l6s710pjtJZVOAO93nM3xT3q5n8dIkhrUMbfdFODvehmY4CE8cX7XFvXfO47VdebbG\nQ9halhdoAprQDcmiI1KEPWGir11H78un8uKGcnJ5iWl48JgODYvd67r3znlTIrwMzXBfOwMe+v1y\nBDq9XV6SvZLauWmgwC9/XkbNkU8P2C/oCRIwA6WcMq/udXPKZljbpJk1GoVCoThE0DSNiooKQqEQ\n3d3dJbHl8XgwjIlJLtZ1vWQW29PTQywWQ9f1ceeYDUVjo051tUM4vG+mJBiUNDbOrErAqcLQDCLe\nCBFvhPll8ynYBZL5JLFsjO6sGxErbuc3/ZNeMakbkkJeY8nyBLFuD44tQAQJBDO0NPu5cK6Pd+e/\nRUq0ExeNxEQjSc9OPPp2EvkER9Wa1DgJXni2AmPNL8jUPYadbqDVE8XIV7H79QZuuyvHmpVeVh2p\nY5gTP2MmJTTtDrB1c4RTz+qkpdmPbkhsS5BJ6xRyIeoXpOlsCRP1RQfsW7AL9GZ76Uh1DFhu6AZB\n0xVlpmMSKExvE3ElvBQKhWIS8Xg8zJkzZ1LPYRgG1dXVlJWV0dXVRSKRwOPxTHgFZEODTWenNkB4\npVKChoaZbycxFZi6Sbm/nHJ/OYtYRN7Ok8qniGVjdGW6yNv5SbeucNsXmdTM2Wd+m0rq1NVnWHtq\nN2tPLW3ZdzsJKSVd2S7KvX50rYnNz0fZVrUbs6wTWdZJDLAtgVUu+GvS5uGHlrH0Z//G0pUJ1p7W\nxkv6ryjzlFHmLaPcW06Zp4yoNzriHLhCQfDGtjBbt0R4dUuEZMJAaNCwKFW6nkVLk6SSBs2NAXZu\nD7LsqMQBxzF1E1M3CZgDhZUtbfKW+7eIp+J4Qh7qqBvLyzshTJrwEkL8FHgb0C6lXNW3rAL4DbAQ\n2AVcJqXsmawxKBQKxeGEx+Ohrq6OaDRaSvL3+XwjTvI/GNdck+Kmm9wquWBQkkoJ0mnBNdekJuT4\nhxoe3YPH73GFWPkiclaOdCFNT7aHrkxXydDVo3smTIjt376omJ/1jit2DrmPEIIqf9WAY+z99mcx\nyveglzeRdLrJiB5OeNM2vJVteJIhqmtjbNsSoWZphheNF7EsQbzXJBS28Hhc2xG/6WdN/lo2/P5c\nWpr9RJY+z5o3v8TRKwVavgzdKqOhziQdD/GrnyzE63NYtiLO8qPjLFuZwB+w97sei6qaLG0tfi68\neO+IXxNd6OiGjhcvhWxhLC/rhDJpyfVCiDOBJPCLfsLrm0C3lPIbQojPAeVSys8e7FgquV6hUChG\nh5SSVCpFR0fHkEn+Y+GppzzcdluQxkZ93BVmhzPFNkfpQtq1rujnIVZsbySEQBNun9HRiLKJqEgc\nyTGkhHQuy7b4y2zZXuCxv4Pl6UKPtOGtaMXBxvrzLUTsBQSCNrvKbydWeT/BsIV0BKFwgfqGjDtl\nay3ikyddjW64mmR903q8upeQGaJ5ex2P/3kpXbvmU18nefvlTRx7QgzHgY42L7V1uRFfV0+8h6Xz\nl3LMwmNG9XqMlmmrahRCLAT+1E94vQqcLaVsEULUAY9IKY882HGU8FIoFIqx4TgOiUSCrq6uKauA\nVIyeoodYquBOTRY9sGzHxpIWtmMzmu/r4pSm3/RPmQlsT7fJts1lbNsSYcdrQba+ZjOnyiRaJmna\nHSAWfppC+RY80S5WntiIr7wLx9NLwS7QEG7gulXXAWA7Njc+c+MBx9c1nUWRRZw590wWly1m/d9q\nePT+Wq64ejfLj46PbIyHofCKSSmj/db3SCkHrekUQlwHXAfQ0NBw/O7duydtnAqFQnGoY9s2sViM\nnp6Zl91RLDhQDI+UEgcHRzo4Tt/9fs8lElvaWLZFIpegO9ONg4OpublPU9XsOpPR+Mh7TmTu/DRC\nQG/Mg3QgELJI9Jr81x3PlbbN23nyTp6QGSo9f7LlSVKFFMlCsnTrynYhpeQDKz7AsugyUkmdH/6P\nQXurhyveqXP8ybGDjmsmCK8Z+06XUv4Y+DG4Ea9pHo5CoVDManRdp7KykrKyslFFTiYTKSXpdJpY\nLEY6nUYIgdfrVRG5IRBCoKO7044jeInqwnXY0iaZS9KZ7qQz3YktbUzNnPQqS7/fYdGSJD3dJsGQ\nTVnUnY4uJvr3p+jF1f/5unnrDjhmqpDi1dirLIosAiAYsplz3u1seWkHN79Qwwk9R3DRKfNYHFmM\nrs3cStupFl5tQoi6flON7VN8foVCoTismWmRJY/HQ1lZGfn8/2/v3mMcO886jn+fc3y3537Z+43c\nlQkbolWQaEWCKFXCH6QUBSUCKVChACKoRagq4p8WJESFSBVBuCiFihKaVIGQNH+hpiKhrVS1JFGa\nbEl6yWXTzWV2du72ju2x/fCHPc7sdnaSHdvnzHh+n92R7WN7/Myrd0fPnvc571NleXmZpaUl6vU6\niUSivWO/bF1oIUOZIYYyQxwbOUaxWmT23Cwz52aoNWqEFpJL5nqy19VWCv03k0/muWHihvOOjeeG\nuObykO+/Ns233ppl+oWnyGcSXDl8JScmT3D58OUd/xzdFvW/wCeAu4DPtm6/EvHni4jINrN2piud\nTjM6Okq5XGZxcZFSqYS7tzeZlc4EFrT3HTs6fJTiapH5lXmmS9OsVle7noQdP7HA7/3xDy8o0n+t\nq5uw3nr0Vm45cgunr3qTb7/2Cm/zAtPnpjk5e5KDhYPtxGupukStUdsWTc97eVXjw8DNwDgwDXwa\neBx4BDgMvAHc7u5z7/W9VFwvIrL71Ov19lJkuVwmCAJSqVQk/Sl3k7WelAvlBd4pvkOlVsHMyCVy\n26If5aV6+pvOt155ld/5tTEmCsMAfO3HX+Pp009zWeEyPvnBT/ZnjZe733mRp36xV58pIiL9IwxD\nBgYGGBgYoFqtUiqV2klYGIakUqlLqgdz9/O+Go3Gefe3i6hr3cyMfDJPPplnf2E/5VqZhfIC06Vp\n5svNizHWzhQZRhiEJIIEgQWEQdjzHfkvVdbHOffccR5fKPGbd79GNtu88CCdSDOWHos7PDXJFhGR\nncPdqVQq7Xowd8fMNr1gYO010EzmwjAkCIL2/bXH26Wov16vMzc3RxAEPWv/9H5VapVmw+pGrb0D\nfLlWplKvUK1XqdQr1Oq1Dd97YZK20fPAhnV8Gx7D3vdVmS8+N8x/PHiI8T0V7vr9Vxkcam7JMbM4\nw9TRqf484yUiItJta83AM5kMY2NjrKysUK1W24mUmREEQft2/f2dVKg/MDDA2bNnWV5e7mr3gUuV\nTqRJk970Ne7e3mus1qj9RJJWrVepNWp460/z77uJcsNbZx7XHVt77fqEut6oU/c6+WT+PZdAr7th\ngUyuxsP/dJTP33c593zqB6QzkA43/1mioMRLRER2pCAIyOfz5PP5uEPpumQyyb59+xgaGmJ6eppq\ntbptN781M5KWJBn09gIId2e+PM+phVPMlefIJ/KkExdPpK64usjH/vAVTr2SJ51p8N1nhvn3f7uK\nxbOjXHs13HMP3HRTT0PekJYaRUREtrFGo8HCwgKzs7MkEgnS6fjP2sRpfQK2Ulshl8htmoBBswXS\n3/zlVYRhlQP7Q6wxRKkE997bm+Rrs6XG7Zc6i4iISFsQBIyOjnLkyBFSqRTFYpFabeO6qt3AzBjN\njnL93uu5ZvwaMJgvz1OulS/6nse/fJDScsjyUhoCGByEfB7uvz/CwFu01CgiIrIDpFIp9u/fT7FY\nZGZmhmq1Sjab3VG1a91kZoxkRxjODLNYWWwvQeYSOTKJ8y9KeOfNLEcvK1Gt1TCyABQK8NrW9nLt\niBIvERGRHcLMGBgYIJfLMT8/z/z8PMlkklRq5+231S1mxnBmmKE9QyxVlji1eIq5lTlyyXcTsH0H\nVpifS5LKvLttSLEIx45FH6+WGkVERHaYMAwZHx/n8OHDhGFIsVikXq/HHVaszIyhzBDXTV7H1OQU\niSDBfHmeldoKt91xmvJKgnOlBN6ApSUolZoF9lFT4iUiIrJDpdNpDh48yN69e6lWq6ysrGybJuhx\nWUvApianmJqcIhWmODT1Kr/9iZMMjVQ5ezbJ5GTvCuvfi5YaRUREdjAzY3BwkFwux9zcHIuLi+pv\nSWtc0oNMTU6xXFlm+Gff4MAV/83xY8d7voHqZpR4iYiI9IFEIsHk5CQDAwPMzMxQKpW21FqpW9yd\narW66RLo2tm59RcImFn78YX3t5pMDqQHuHbiWibTk4zl4m0bpMRLRESkj2SzWQ4ePEi5XKZUKrG8\nvEy9XsfMSKVSPd0Fv9FoUK1W270v8/k8g4OD7c9c3yvzwsfr+2au9dFc309zdXWVUqnU0dm8QrJA\nPhnvhrtKvERERPpMEATkcjlyuRzj4+NUKhVWVlZYXFykVCoBtJOwTrejqNVqrK6u4u7txuaFQqEn\njb7PnTvHmTNnKJVKZLPZbbmT/3tR4iUiItLH1ve3HBkZYXV1lZWVFZaWltrF+IlEglQq9b6SsLWz\nT2ubuKZSKUZHR8nlcu/7e2xVLpfj8OHDLC0tMTs7C0Amk9lRe5kp8RIREdlFkskkyWSSwcFB6vU6\n5XKZ5eVlSqUS7k4QBD9RF9ZoNNrJlpmRzWYZHR0lm81GXsQfBAHDw8MUCgXm5+dZWFjYUa2UlHiJ\niIjsUmEYthuNNxoNKpXKeXVhQDsZKxQKFAoFMpkMYRjGHHnzYoKJiQkGBweZmZmhWCySyWR6WsPW\nDds7OhEREYlEEARks1my2SxjY2NUq1UqlQrJZLIn9Vrdkk6nOXDgAKVSqd1KKZPJbNt4lXiJiIjI\necyMdDq9Y5bvzIxCoUAul2NxcZHZ2dl2bdt2q/+KJfEys9eBZaAO1Nz9RBxxiIiISP8IgoCRkREK\nhQKzs7MsLS2RSqW2VS/LOM94/YK7n43x80VERKQPJZNJ9u7dy9DQUHsz2UwmE3dYgHo1ioiISJ/K\nZrMcOnSIPXv2sLq6SrVajTuk2BIvB75qZs+a2d0bvcDM7jazZ8zsmZmZmYjDExERkX6w1svyyJEj\nTExMxH7VY1yf/gF3f8vMJoEnzexld//6+he4+wPAAwAnTpzY3a3WRUREpCNhGDI+Ph53GPGc8XL3\nt1q3Z4DHgBvjiENEREQkSpEnXmaWN7OBtfvAh4GTUcchIiIiErU4lhr3AI+19tVIAA+5+3/FEIeI\niIhIpCJPvNz9VeB41J8rIiIiEjdtJyEiIiISESVeIiIiIhFR4iUiIiISESVeIiIiIhEx9+2/N6mZ\nzQCnevwx44B6R/aOxrd3NLa9pfHtHY1tb2l8e+e9xvaIu09s9MSOSLyiYGbPuPuJuOPoVxrf3tHY\n9pbGt3c0tr2l8e2dTsZWS40iIiIiEVHiJSIiIhIRJV7veiDuAPqcxrd3NLa9pfHtHY1tb2l8e2fL\nY6saLxEREZGI6IyXiIiISESUeImIiIhERIkXYGa3mNn3zexHZvYnccfTT8zsdTN70cyeN7Nn4o5n\npzOzL5jZGTM7ue7YqJk9aWY/bN2OxBnjTnWRsf2Mmb3Zmr/Pm9kvxxnjTmZmh8zsKTN7ycy+Z2Yf\nbx3X/O3QJmOr+dshM8uY2XfM7Lutsf2z1vEtz9tdX+NlZiHwA+CXgNPA/wJ3uvv/xRpYnzCz14ET\n7q5N/LrAzH4eKAL/6u5TrWN/Bcy5+2db/3EYcfdPxRnnTnSRsf0MUHT3v44ztn5gZvuAfe7+nJkN\nAM8CHwF+C83fjmwytr+O5m9HzMyAvLsXzSwJfBP4OPBRtjhvdcYLbgR+5O6vunsV+DJwW8wxiWzI\n3b8OzF1w+Dbgi637X6T5C1cu0UXGVrrE3d929+da95eBl4ADaP52bJOxlQ55U7H1MNn6cjqYt0q8\nmpPzx+sen0YTtpsc+KqZPWtmd8cdTJ/a4+5vQ/MXMDAZczz95h4ze6G1FKllsC4ws6PAzwDfRvO3\nqy4YW9D87ZiZhWb2PHAGeNLdO5q3SrzANji2u9dfu+sD7n4DcCvwB63lHJGd4h+Ay4DrgbeBe2ON\npg+YWQF4FPiEuy/FHU8/2WBsNX+7wN3r7n49cBC40cymOvl+SryaZ7gOrXt8EHgrplj6jru/1bo9\nAzxGc2lXumu6VeOxVutxJuZ4+oa7T7d+6TaAz6P525FWjcyjwJfc/T9bhzV/u2CjsdX87S53XwCe\nBm6hg3mrxKtZTH+FmR0zsxRwB/BEzDH1BTPLtwo9MbM88GHg5Obvki14Arirdf8u4CsxxtJX1n6x\ntvwqmr9b1ipS/mfgJXf/3LqnNH87dLGx1fztnJlNmNlw634W+BDwMh3M211/VSNA6xLb+4AQ+IK7\n/0W8EfUHM/spmme5ABLAQxrbzpjZw8DNwDgwDXwaeBx4BDgMvAHc7u4qEr9EFxnbm2ku0zjwOvC7\na3UdcmnM7IPAN4AXgUbr8J/SrEXS/O3AJmN7J5q/HTGzn6ZZPB/SPFn1iLv/uZmNscV5q8RLRERE\nJCJaahQRERGJiBIvERERkYgo8RIRERGJiBIvERERkYgo8RIRERGJSCLuAEREesHM6jQvr08CNZqX\nhN/X2kxSRCQWSrxEpF+ttNp8YGaTwEPAEM39uUREYqGlRhHpe62WVXfTbBhsZnbUzL5hZs+1vn4O\nwMweNLPb1t5nZl8ys1+JK24R6T/aQFVE+pKZFd29cMGxeeBqYBlouHvZzK4AHnb3E2Z2E/BH7v4R\nMxsCngeucPda1PGLSH/SUqOI7CbWuk0C95vZ9UAduBLA3f/HzP6utTT5UeBRJV0i0k1KvERkV2j1\nDq0DZ2jWeU0Dx2mWXJTXvfRB4DeAO4CPRRymiPQ5JV4i0vfMbAL4R+B+d/fWMuJpd2+Y2V00G+Cu\n+RfgO8A77v696KMVkX6mxEtE+lXWzJ7n3e0kHgQ+13ru74FHzex24CmgtPYmd582s5eAxyONVkR2\nBRXXi4isY2Y5mvt/3eDui3HHIyL9RdtJiIi0mNmHgJeBv1XSJSK9oDNeIiIiIhHRGS8RERGRiCjx\nEhEREYmIEi8RERGRiCjxEhEREYmIEi8RERGRiPw/oy9YLqO7LsQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1000x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "posterior_samples = surrogate_posterior.sample(50)\n",
        "param_samples = posterior_samples[:-1]\n",
        "unconstrained_rate_samples = posterior_samples[-1][..., 0]\n",
        "rate_samples = positive_bijector.forward(unconstrained_rate_samples)\n",
        "\n",
        "plt.figure(figsize=(10, 4))\n",
        "mean_lower, mean_upper = np.percentile(rate_samples, [10, 90], axis=0)\n",
        "pred_lower, pred_upper = np.percentile(\n",
        "    np.random.poisson(rate_samples), [10, 90], axis=0)\n",
        "\n",
        "_ = plt.plot(observed_counts, color='blue', ls='--', marker='o',\n",
        "             label='observed', alpha=0.7)\n",
        "_ = plt.plot(np.mean(rate_samples, axis=0), label='rate', color='green',\n",
        "             ls='dashed', lw=2, alpha=0.7)\n",
        "_ = plt.fill_between(\n",
        "    np.arange(0, 30), mean_lower, mean_upper, color='green', alpha=0.2)\n",
        "_ = plt.fill_between(np.arange(0, 30), pred_lower, pred_upper, color='grey',\n",
        "    label='counts', alpha=0.2)\n",
        "plt.xlabel('Day')\n",
        "plt.ylabel('Daily Sample Size')\n",
        "plt.title('Posterior Mean')\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0aoMoQyf_fWC"
      },
      "outputs": [],
      "source": [
        "forecast_samples, rate_samples = sample_forecasted_counts(\n",
        "   sts_model,\n",
        "   posterior_latent_rates=unconstrained_rate_samples,\n",
        "   posterior_params=param_samples,\n",
        "   # Days to forecast:\n",
        "   num_steps_forecast=30,\n",
        "   num_sampled_forecasts=100)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eQ7zJpEr_hHU"
      },
      "outputs": [],
      "source": [
        "forecast_samples = np.squeeze(forecast_samples)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lcEpkAEi_jcn"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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XX0JVFWzfDmvXhp7/ZowxxnQVoUxZ/hQ4GigBcM6tBga0eEY3JQIX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\n",
            "text/plain": [
              "<Figure size 1000x400 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plot_forecast_helper(observed_counts, forecast_samples, CI=80)"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "STS_approximate_inference_for_models_with_non_Gaussian_observations.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
